Defining functions Lesson Topic

Lesson: Defining functions

Lesson Topic: Define functions

Fill in the blank:

Typically, the x-value in a function is called the ______.

Expression

Axis

Input

Variable

Output

Question 1:

Fill in the blank:

A function is a mathematical rule that _________________.

Has one or more exponential expressions

Sends every input to only one output

Can be graphed as a straight line

Sends every output to only one input

Question 2:

Fill in the blank:

A relation is not a function if __________________.

The graph of the relation is not straight

An output matches more than one input

One input is sent to two different outputs

It is represented by a table

It has two variables

Question 3:

Which of the following ways can a function be represented?

A collection of points

A table

An equation

A graph

all of the above

Question 4:

Fill in the blank:

Typically, the y-value in a function is called the ______.

Variable

Output

Axis

Input

Expression

Question 5:

Lesson Topic: Identify domain and range

State the domain for the set of points.

{(8, 8), (5, 7), (-4, 8), (4, 8)}

Domain = {-4, 4, 5, 8}

Domain = {7, 4, 5, 8}

Domain = {-7, 4, 5, 8}

Domain = {-8, 4, 5, 8}

Question 1:


{(-38, -7), (29, -76), (-69, -28), (-64, 9), (29, -7), (-69, -76)}

Domain = {-69, -64, -7, 29}

Domain = {-38, 9, -69, 29}

Domain = {-38, -76, -69, 29}

Domain = {-69, -64, -38, 29}

Question 2:


{(11, -96), (-56, -96), (166, -136)}

Domain = {-56, -136, 166}

Domain = {-136, 11, 166}

Domain = {-56, 11, -96}

Domain = {-56, 11, 166}

Question 3:

State the range for the set of points.

{(167, 183), (-58, 175), (173, 141), (-49, 141)}

Question 4:

Range = {167, 175, 183}

Range = {-58, 175, 183}

Range = {141, 175, 183}

Range = {141, -49, 183}


{(-40, -105), (2, 84), (-62, 71), (30, -94), (-20, 71), (-40, -110)}

Range = {-110, -105, -94, 71, 84}

Range = {-62, -110, -94, 71, 84}

Range = {-105, -110, -94, 71, 30}

Range = {-105, -40, -94, 71, 84}

Question 5:


{(48.9, -53.3), (84.6, -19.9), (-62.6, 81.7), (-14.4, -42.6), (71.2, -84.1), (71.2, 76.8)}

Domain = {-53.3, -14.4, 48.9, 71.2, 84.6}

Domain = {-14.4, -62.6, 48.9, -42.6, 84.6}

Domain = {-62.6, -14.4, 48.9, 71.2, 84.6}

Domain = {-14.4, -62.6, 48.9, 71.2, 84.1}

Question 6:


{(48.9, -53.3), (84.6, -19.9), (-62.6, 81.7), (-14.4, -42.6), (71.2, -84.1), (71.2, 76.8)}

Range = {-84.1, 48.9, -42.6, -53.3, 76.8, 81.7}

Range = {-19.9, -42.6, -53.3, -14.4, 76.8, 81.7}

Range = {-84.1, -53.3, -42.6, -19.9, 76.8, 81.7}

Question 7:

Range = {-19.9, -42.6, -53.3, -84.1, 76.8, 71.2}


{(-4, 9), (8, 9), (5, -7), (-6, 1), (2, -7)}

Range = {-7, 1, 9}

Range = {-7, -6, 9}

Range = {-7, -4, 9}

Range = {-7, 2, 9}

Question 8:


{(35.8, -111.6), (98.4, -103.4), (35.8, 99.4), (103.1, -111.8), (1.5, 113.5), (-47.3, -103.4)}

Domain = {-47.3, 1.5, 103.4, 35.8, 98.4}

Domain = {-47.3, 1.5, 103.1, 103.4, 98.4}

Domain = {-47.3, 1.5, 35.8, 98.4, 103.1}

Domain = {-47.3, 1.5, 103.1, 35.8, 113.5}

Question 9:


{(173, -154), (169, -138), (186, -154), (72, 178), (35, 184), (-32, -159)}

Domain = {-32, 169, 173, 186, 35, 184}

Domain = {-32, 35, 72, 169, 173, 186}

Domain = {-32, 72, 173, 186, 35, 72}

Domain = {-32, 169, 173, 186, 35, -154}

Question 10:

Lesson Topic: Determine if a relation is a function from a data table

Determine if the rule given by the following table represents a function or is not a function.

Function

Not a function

Question 1:


Function

Not a function

Question 2:


Question 3:

Function

Not a function


Function

Not a function

Question 4:


Question 5:

Function

Not a function


Function

Not a function

Question 6:


Function

Not a function

Question 7:


Question 8:

Function

Not a function


Function

Not a function

Question 9:


Question 10:

Function

Not a function

Lesson Topic: Determine if a relation is a function on a graph

Determine if the following relationship is a function or is not a function.

Function

Not a function

Question 1:


Question 2:

Function

Not a function


Function

Question 3:

Not a function


Function

Not a function

Question 4:


Question 5:

Function

Not a function


Function

Question 6:

Not a function


Function

Not a function

Question 7:


Question 8:

Function

Not a function


Function

Question 9:

Not a function


Function

Not a function

Question 10:

Lesson Topic: Determine if a relation is a function from a collection of data points

Determine if the following collection of points represents a function or does not represent a function:

{(0,2), (1, 5), (2, 14), (7, 2)}

Function

Not a function

Question 1:


{(7,1), (1, 11), (-2, 10), (7, 2)}

Function

Not a function

Question 2:


{(20,1), (14, 4), (9, 9), (4, 14)}

Function

Not a function

Question 3:


{(1,1), (2, 3), (1, 2), (-2, 4)}

Function

Not a function

Question 4:


{(6,1), (7, 4), (8, 9), (7, 9)}

Function

Not a function

Question 5:


{(3,2), (6, 4), (9, 6), (12, 8)}

Function

Not a function

Question 6:


{(5, 15), (6, 15), (7, 15), (9, 15)}

Function

Not a function

Question 7:


{(0, 9), (5, 7), (10, 5), (15, 3)}

Function

Not a function

Question 8:


Question 9:

{(2, 9), (3, 4), (4, 9), (3, 9)}

Function

Not a function


{(1, 10), (4, 11), (8, 12), (12, 12)}

Function

Not a function

Question 10:

Lesson Topic: Use a function rule to determine outputs from an input Part 1

What is the output, or y-value, when you input x = 7 into the function:

y = 4x + 1

y =

Question 1:


y = 1 − x

y =

Question 2:


y = (1⁄5)x + 2

y =

Question 3:

What is the output, or y-value, when you input x = -1 into the function:

y = 3x

y =

Question 4:


y = 2x + 6

y =

Question 5:


y = 4x

y =

Question 6:


y = 3 − x

Question 7:

y =


y = 2x − 3

y =

Question 8:


y = 2x − 2

y =

Question 9:


y = 3x + 6

y =

Question 10:



y = x2 − 41

y =

Question 1:


y = 3x2 + 5

y =

Question 2:


y = x2 − 2x + 5

y =

Question 3:


y = x2 + 8x − 19

y =

Question 4:


y = x2 + 6x + 9

y =

Question 5:


y = x2 + x − 60

y =

Question 6:


y = x2 + 7x + 12

Question 7:

y =


y = 2x2 + 5x − 3

y =

Question 8:


y = x2 − 2x − 15

y =

Question 9:


y = x2 + 4x + 4

y =

Question 10:



y = 4x3 + 3.

y =

Question 1:


y = x4 − 5x2 + 40

y =

Question 2:


y = x4 − 2x3 + x2 + 4x − 10

y =

Question 3:


y = x3 + x2 − 4x − 16

y =

Question 4:


y = x3 + x2 + 2x + 5

y =

Question 5:


y = x3 − 350

y =

Question 6:


y = x5 + 63

Question 7:

y =


y = x5 + 4x2

y =

Question 8:


y = x4 − 6x2

y =

Question 9:


y = x4 − 2x3.

y =

Question 10:

Lesson Topic: Test specific points to determine if a rule is a function

x y

-3 0

-3

0 3

3

Show that the relation y2 + x2 = 9 is not a function by filling in the table of values.

Question 1:

Solve for x in the following equation:

x2 = 36

x = 6

x = 6 and x = -6

x = -6

Question 2:

x y

10

10 -1

-2

18 3

Show that the relation y2 + 9 = x is not a function by filling in the table of values.

Question 3:

x y

2

4 3

Show that the relation 5 = y2 − x is not a function by filling in the table of values.

Question 4:

31 -6

31

A class is given the relation y2 = x, and input x = 9. Together, they substitute to find the output:

y2 = (9)

Andrew correctly wrote that a possible output is y = 3, but the teacher said there is another possible output in this

relation. What is another possible solution for y?

y =

Question 5:

x y

-2 5

-5

14 3

19

Show that the relation y2 + x = 23 is not a function by filling in the table of values.

Question 6:

A class is given the relation y2 + x2 = 25, and input x = 0. Together, they substitute to find the output:

y2 = 25

Mindy correctly wrote that a possible output is y = -5, but the teacher said there is another possible output in this

relation. What is another possible solution for y?

y =

Question 7:

x y

0 5

-5

3

Show that the relation y2 + x2 = 25 is not a function by filling in the table of values.

Question 8:

3 -4

x y

-6 4

-4

3

1 -3

Show that the relation y2 + x = 10 is not a function by filling in the table of values.

Question 9:

x y

-9 9

-9

10 -10

10

Show that the relation y2 = x + 90 is not a function by filling in the table of values.

Question 10:

Lesson Topic: Determine if a relation is a function in an equation by testing points

Determine if the following equation represents a function:

y = -3x2 + 5

Function

Not a function

Question 1:


x2 + y2 = 16

Function

Not a function

Question 2:


y2 − x2 = 36

Function

Not a function

Question 3:


x2 + y2 = 9

Function

Not a function

Question 4:


y = 4x2

Question 5:

Function

Not a function


y2 − x2 = 100

Function

Not a function

Question 6:


y = 17 − 20x

Function

Not a function

Question 7:


y = x3

Function

Not a function

Question 8:


y = 5x + 15

Function

Not a function

Question 9:


Question 10:

y2 = x + 16

Function

Not a function

Lesson: Functions

Lesson Topic: Understand function notation

In the function f(x) = 2x, f(x) is which of the following?

The output

Always 0

Undefined

The input

The domain

Question 1:

In the function f(x) = 3⁄2 x, x is which of the following?

The y-intercept

The output

The input

Question 2:

The range

The slope


Only 0, 5, 10, or 15

The domain

The output

The input

The same as x

Question 3:

The circled values are part of the function's:

Check all that are true.

Input

Question 4:

Output

Domain

Range

Square root


The function

The input

The domain

The output

The outsource

Question 5:

The circled values are part of the function's:

Question 6:

Check all that are true.

Input

Output

Domain

Range

Name


The output

The function

Both the input and the output

The input

The domain

Question 7:

For each input value:

The output value is 4.

There is only one output value.

There are no output values.

There are two output values.

There can be many different output values.

Question 8:


The output

The y-intercept

The slope

The range

Question 9:

The input


The range

The input

1⁄3

The output

The inversion

Question 10:

Lesson Topic: Calculate functions Part 1

For the function f(x) = 3x

Find f(4) =

Question 1:

For the function f(x) = 5x + 4

Find f(6) =

Question 2:

For the function f(x) = 4x − 7

Find f(-3) =

Question 3:

For the function f(x) = x2

Find f(5) =

Find f(-5) =

Question 4:


Find f(5) =

Question 5:

For the function f(x) = x3

Find f(2) =

Find f(-2) =

Question 6:


Find f(6) =

Question 7:

For the function f(x) = 3⁄4 x

Find f(4) =

Question 8:

For the function f(x) = 4x + 7

Find f(3) =

Question 9:

For the function f(x) = 1⁄2 x + 1

Find f(2) =

Question 10:


For the function: f(x) = 10 + 7x + 5x2

Find f(2) =

Question 1:

For the function: f(x) = 12 + 10x − 5x2

Find f(-6) =

Question 2:


Find f(3) =

Question 3:

For the function: f(x) = 12 + 3x − x2

Find f(5) =

Question 4:


Find f(-4) =

Question 5:

For the function: f(x) = 17 − 7x + 2x2

Find f(7) =

Question 6:

For the function: f(x) = 3 + x + 4x2

Find f(9) =

Question 7:


Find f(2) =

Question 8:

Question 9:

For the function: f(x) = 15 + 4x − x2

Find f(5) =


Find f(6) =

Question 10:

Lesson Topic: Calculate functions word problems

At a concession stand, the first cup of iced tea costs $2.25, and refills cost $0.15 each. If one customer

ordered a cup of iced tea and 2 refills, how much did the customer pay?

$

Question 1:

A gym membership costs a flat fee of $68 and an additional $19.99 per month. Since she became a member,

Ellen has paid the gym $207.93. How many months has Ellen been a member of the gym?

months

Question 2:

A moving truck rental costs a flat fee of $75 and $2 per mile driven. If you drive a moving truck for 10 miles,

how much is the rental for the moving truck?

$

Question 3:

At a lemonade stand, the first cup costs $1.50, and refills cost $0.20 each. If a customer paid $1.90 in total for

his first cup and refills, how many refills did the customer order?

refills

Question 4:

During a storm, the distance in feet between the lightning and your location was represented by f(x) = 1,200x,

where x is the number of seconds between the lightning and thunder. At one point, you counted 4 seconds

between the lightning and the thunder. How far were you from the lightning?

ft

Question 5:

Alexis has come up with the equation, f(x) = -2x + 20, to calculate how many bottles of lotion are left after

assembling gift baskets. The variable x represents the number of gift baskets assembled and f(x) represents

the number of bottles of lotion left. If 6 bottles of lotion are left, how many gift baskets were assembled?

gift baskets

Question 6:

A gym membership costs a flat fee of $50 and an additional $35 per month. If you have been a member of the

Question 7:

gym for a year and a half, how much have you paid for your membership in total?

$

Bob's age is 3 times greater than Susanne's age. If Susanne's age is 4 years old, how old is Bob?

years old

Question 8:

A soft drink costs $1.65 and each refill for the drink costs $0.95. If you have $4.50, how many refills can you

purchase?

refills

Question 9:

A gym membership has a starting fee of $58 and a monthly fee of $14.99. If you purchase a membership of 7

months, how much will the membership cost?

$

Question 10:

Lesson Topic: Complete function tables

x f(x)

0

11

17

3

Complete the function table.

Function: f(x) = 6x + 5

Question 1:

x f(x)

4

31

6

43



Question 2:

x f(x)

0

2

17

6



Question 3:


Question 4:

a f(a)

9

2

13

4

Function: f(a) = 2a + 7

h f(h)

9

10

2

12


Function: f(h) = h + 9

Question 5:

z f(z)

3

21

9

45


Function: f(z) = 4z − 3

Question 6:

r f(r)

4


Function: f(r) = 1⁄2 r − 2

Question 7:

6

2

3

j f(j)

3

10

13

18


Function: f(j) = j − 2

Question 8:

c f(c)

0

6

9

27


Function: f(c) = 3c − 9

Question 9:

b f(b)

3

16

7

24


Function: f(b) = 2b + 6

Question 10:

Lesson: Construct functions to model linear relationships

Lesson Topic: Identify rate of change from an equation in slope-intercept form

Find the rate of change, or slope, in the following equation:

y = -2x − 10

The rate of change is m =

Question 1:


y = -8x + 12


Question 2:


y = (1⁄4)x + 2


Question 3:


y = -2x + 1⁄5


Question 4:


y = 9x − 2


Question 5:


y = x + 6


Question 6:

Question 7:


y = -3x − 2⁄3



y = -6x + 10


Question 8:


y = 12x − 20


Question 9:


y = 7x − 5


Question 10:

Lesson Topic: Identify initial value or y-intercept from slope-intercept form

Find the initial point, or y-intercept, in the following linear function:

y = (1⁄3)x + 5

The initial point of the function is b =

Question 1:


y = -(5⁄9)x − 6


Question 2:


y = 3x − 1


Question 3:


y = -2x + 12


Question 4:


y = -6x + 7


Question 5:


y = (1⁄5)x + 7

Question 6:



y = 12x − 5


Question 7:


y = -7x − 11


Question 8:


y = 19x + 3


Question 9:


y = 4x − 11


Question 10:

Lesson Topic: Derive a function from a function table Part 1

Which linear equation matches the function table?

y = 3⁄2x

y = 3x

y = 2⁄3x

y = 3⁄2 + x

y = 2x

Question 1:


y = 2⁄3x

y = 3⁄6x

y = 3⁄2 + x

y = 3x

y = 2x

Question 2:


y = 1⁄4x

y = 3⁄4x

y = 3x

y = x + 4

y = 4x

Question 3:


y = 5⁄2x

y = 2⁄5x

y = 2x

y = 5x

y = x + 5⁄2

Question 4:


y = 5⁄2x

y = x + 5⁄2

y = 2⁄5x

y = 2x + 5

y = 2x

Question 5:


y = 7x + 3

y = x + 3⁄7

y = 3⁄7x

y = 7x

y = 7⁄3x

Question 6:

Question 7:


y = 1⁄5x

y = 5⁄10x

y = 5x + 1

y = 5x

y = x


y = x

y = x + 6

y = 1⁄6x

y = 6x

y = 1⁄12x

Question 8:


y = 4⁄3x

y = 3⁄4x

y = -3⁄4x

y = 3x

y = 4x

Question 9:


y = 1⁄4x

y = 4x

y = 2⁄4x

y = 1⁄2x

y = 4⁄2x

Question 10:


Fill in the y-intercept to complete the function equation.

y = 1⁄2 x +

Question 1:


y = 3⁄2 x +

Question 2:


y = 4x +

Question 3:


y = 3⁄4 x +

Question 4:


y = 3x +

Question 5:


y = 1⁄3 x +

Question 6:


y = 4x +

Question 7:


y = 5x +

Question 8:


y = 2⁄5 x +

Question 9:


y = 2⁄3 x +

Question 10:



y = 1⁄2 x +

Question 1:


y = 3⁄2 x +

Question 2:


y = 4x +

Question 3:


y = 3⁄4 x +

Question 4:


y = 3x +

Question 5:


y = 4x +

Question 6:


y = 1⁄3 x +

Question 7:


y = 5x +

Question 8:


y = 2⁄5 x +

Question 9:


y = 2⁄3 x +

Question 10:


Which function equation matches the function table?

y = 1⁄2x + 1

y = 3x + 1

y = 2x + 1

y = 2x + 3

y = 1⁄2x − 1

Question 1:


y = 1⁄4x + 3

y = 4x − 3

y = 3⁄4x + 3

y = 1⁄2x + 3

y = 3x + 4

Question 2:

Question 3:


y = 1⁄2x + 2

y = 1⁄3x + 2

y = 2x − 1

y = 2x + 2

y = 1⁄2x + 3


y = 4x − 6

y = 3⁄4x − 6

y = 2x + 6

y = 4x + 6

y = 1⁄4x + 6

Question 4:


y = 5x + 1

y = -1⁄5x + 5

y = 1⁄5x + 5

y = 1⁄4x + 5

y = x + 5

Question 5:


y = 2x − 8

y = 1⁄2x + 8

y = 3⁄2x − 8

y = 2x + 8

y = -2x + 8

Question 6:


y = 3⁄4x + 2

y = 3x + 2

y = 3⁄4x − 2

y = 4⁄3x + 2

y = 2x + 4

Question 7:


y = 1⁄2x − 3

y = -2x + 3

y = 3x + 3

y = 1⁄2x + 3

y = 2x + 3

Question 8:


y = 7x − 4

y = 7x + 4

y = x + 4

y = 3⁄7x + 6

y = 1⁄7x + 4

Question 9:


y = 5x + 6

y = 5⁄6x − 5

y = 6x − 5

y = -5x + 5

y = 6x + 5

Question 10:

Lesson Topic: Find a rate of change from a graph of a linear equation

What is the rate of change of the linear function in the following graph?

m =

Question 1:


Question 2:

m =


Question 3:

m =


Question 4:

m =


Question 5:

m =


Question 6:

m =


Question 7:

m =


Question 8:

m =


Question 9:

m =


Question 10:

m =

Lesson Topic: Find the initial point from a graph of a linear equation

What is the initial point, or y-intercept, of the linear function shown in the following graph?

The initial point, or y-intercept, is at (0, ).

Question 1:


Question 2:



Question 3:



Question 4:



Question 5:



Question 6:



Question 7:



Question 8:



Question 9:



Question 10:


Lesson Topic: Derive functions from graphs

Which of the following linear equations matches the graph?

y = 2x

y = -2x

y = (1⁄2)x

y = -(1⁄2)x

y = x⁄3

Question 1:


y = -x

Question 2:

y = x

y = -(1⁄3)x

y = 3x

y = -(1⁄2)x


y = -(2⁄3)x

y = -(3⁄2)x

y = (2⁄3)x

y = (3⁄2)x

y = -3x

Question 3:


y = -2x

y = x

y = (1⁄2)x

y = -x

y = 2 ÷ x

Question 4:


y = -3x

y = -(1⁄2)x

Question 5:

y = 2x

y = 3x

y = x


y = -5x

y = (1⁄5)x

y = 5x

y = -(1⁄5)x

y = 0x

Question 6:

Question 7:


y = 3⁄x

y = 6x

y = 3x

y = 1⁄3 x

y = 2x


y = (1⁄2)x

y = 2x

y = -x

y = -(1⁄2)x

y = x

Question 8:


y = (1⁄3)x

y = -3x

y = 3x

y = -(1⁄3)x

y = -x

Question 9:


y = 2⁄3 x

y = -2x

Question 10:

y = 6x

y = -x⁄3

y = -3⁄2 x

Lesson Topic: Complete a table to represent function values in a word problem

Jon uses 6 centimeters of tape on each present he wraps. Complete the table to determine the amount of

tape used for different amounts of presents wrapped.

Presents Amount of Tape (cm)

1

2

3

4

Question 1:

A construction company has 80 crates of screws and uses 4 crates per house that the company builds.

Complete the table to determine the number of crates that are left after each number of houses are built.

Number of Houses Number of Crates

1

2

3

4

Question 2:

To rent headphones, you pay a deposit of $6 and then $2 per hour. Complete the table to determine the cost

of renting headphones for 1, 2, 3, or 4 hours.

Hours Cost ($)

1

2

3

4

Question 3:

A company charges $25 a day for a car rental along with a $60 one time fee. Complete the table to determine

Question 4:

the cost to rent the car for 1, 2, 3, or 4 days.

Days Cost ($)

1

2

3

4

A construction company has 94 crates of screws and uses 4 crates per house built. Complete the table to

determine the number of crates left after 1, 2, 3 and 4 houses are built.

Houses Number of Crates Left

1

2

3

4

Question 5:

Troy can make 7 liters of jam per day. Complete the table to determine the amount of jam Troy can make in 1,

2, 3, and 4 days.

Number of Days Amount of Jam (liters)

1

2

3

4

Question 6:

A tree grows 20 centimeters per year. Complete the table to determine the height of the tree after it has grown

for 1, 2, 3, and 4 years.

Years Height (cm)

1

Question 7:

2

3

4

When online shopping, Alejandro takes 48 seconds to purchase one item. Complete the table with the amount

of time it takes Alejandro to purchase 1, 2, 3, and 4 items.

Number of Items Time (seconds)

1

2

3

4

Question 8:

The pollution level in the center of the city is 30 parts per million. The pollution level grows 25 parts per million

every hour. Complete the table to determine the amount of pollution after 1, 2, 3 and 4 hours.

Number of Hours Pollution (parts per million)

1

2

3

4

Question 9:

A maintenance warranty for solar heaters cost $50 a month plus a one time $15 processing fee. Complete the

table to determine the total cost for different number of months.

Months Total Cost ($)

1

2

3

4

Question 10:

Correct Answers

Lesson: Defining functions

Lesson Topic: Define functions

Question 1:MC3

Question 2:MC2

Question 3:MC3

Question 4:MC5

Question 5:MC2

Lesson Topic: Identify domain and range

Question 1:MC1

Question 2:MC4

Question 3:MC4

Question 4:MC3

Question 5:MC1

Question 6:MC3

Question 7:MC3

Question 8:MC1

Question 9:MC3

Question 10:MC2

Lesson Topic: Determine if a relation is a function from a data table

Question 1:MC1

Question 2:MC2

Question 3:

MC1

Question 4:MC2

Question 5:MC2

Question 6:MC2

Question 7:MC1

Question 8:MC1

Question 9:MC1

Question 10:MC1

Lesson Topic: Determine if a relation is a function on a graph

Question 1:MC2

Question 2:MC1

Question 3:MC1

Question 4:MC2

Question 5:MC2

Question 6:MC1

Question 7:MC1

Question 8:MC2

Question 9:MC2

Question 10:MC2

Lesson Topic: Determine if a relation is a function from a collection of data points

Question 1:MC1

Question 2:MC2

Question 3:MC1

Question 4:MC2

Question 5:MC2

Question 6:MC1

Question 7:MC1

Question 8:MC1

Question 9:MC2

Question 10:MC1


Question 1:y = 4(7) + 1 y = 28 + 1 y = 29

Question 2:y = 1 − 2 y = -1

Question 3:

y = (1⁄5)(5) + 2 y = 1 + 2 y = 3

Question 4:y = 3(-1) y = -3

Question 5:y = 2(-4) + 6 y = -8 + 6 y = -2

Question 6:y = 4(5) y = 20

Question 7:y = 3 − 1 y = 2

Question 8:y = 2(-4) − 3 y = -8 − 3 y = -11

Question 9:y = 2(3) − 2 y = 6 − 2 y = 4

Question 10:y = 3(-2) + 6 y = -6 + 6 y = 0


Question 1:

y = (11)2 − 41 y = 121 − 41 y = 80

Question 2:

y = 3(2)2 + 5 y = 3(4) + 5 y = 12 + 5 y = 17

Question 3:

y = (3)2 − 2(3) + 5 y = 9 − 6 + 5 y = 8

Question 4:

y = (1)2 + 8(1) − 19 y = 1 + 8 − 19 y = -10

Question 5:

y = (-5)2 + 6(-5) + 9 y = 25 − 30 + 9 y = 4

Question 6:

y = (12)2 + (12) − 60 y = 144 + 12 − 60 y = 96

Question 7:

y = (-1)2 + 7(-1) + 12 y = 1 − 7 + 12 y = 6

Question 8:

y = 2(3)2 + 5(3) − 3 y = 2(9) + 15 − 3 y = 18 + 15 − 3 y = 30

Question 9:

y = (-1)2 − 2(-1) − 15 y = 1 + 2 − 15 y = -12

Question 10:

y = (7)2 + 4(7) + 4 y = 49 + 28 + 4 y = 81


Question 1:

y = 4(2)3 + 3 y = 4(8) + 3 y = 32 + 3 y = 35

Question 2:

y = (-2)4 − 5(-2)2 + 40 y = 16 − 5(4) + 40 y = 16 − 20 + 40 y = 36

Question 3:

y = (1)4 − 2(1)3 + (1)2 + 4(1) − 10 y = 1 − 2(1) + (1) + 4(1) − 10 y = 1 − 2 + 1 + 4 − 10 y = -6

Question 4:

y = (4)3 + (4)2 − 4(4) − 16 y = 64 + 16 − 16 − 16 y = 48

Question 5:

y = (-4)3 + (-4)2 + 2(-4) + 5 y = -64 + 16 − 8 + 5 y = -51

Question 6:

y = (7)3 − 350 y = 343 − 350 y = -7

Question 7:

y = (-2)5 + 63 y = -32 + 63 y = 31

Question 8:

y = (2)5 + 4(2)2 y = 32 + 4(4) y = 32 + 16 y = 48

Question 9:

y = (4)4 − 6(4)2 y = 256 − 6(16) y = 256 − 96 y = 160

Question 10:

y = (5)4 − 2(5)3 y = 625 − 2(125) y = 625 − 250 y = 375

Lesson Topic: Test specific points to determine if a rule is a function

Question 1:The relation is not a function because the input 0 can be sent to more than one output.

Question 2:MC2



Question 5:

y = -3 is also a possible solution to y2 = 9 Check: (-3)2 = 9 9 = 9

Question 6:The relation is not a function because the input -2 can be sent to more than one output.

Question 7:

y = 5 is also a possible solution to y2 = 25 Check: (5)2 = 25 25 = 25

Question 8:The relation is not a function because the inputs 0 and 3, both can be sent to more than one output.

Question 9:The relation is not a function because the inputs -6 and 1, both can be sent to more than one output.

Question 10:The relation is not a function because the inputs -9 and 10 can be sent to more than one output.

Lesson Topic: Determine if a relation is a function in an equation by testing points

Question 1:MC1

Question 2:MC2

Question 3:MC2

Question 4:MC2

Question 5:MC1

Question 6:MC2

Question 7:MC1

Question 8:MC1

Question 9:MC1

Question 10:MC2

Lesson: Functions

Lesson Topic: Understand function notation

Question 1:MC1

Question 2:MC3

Question 3:MC3

Question 4:MC1 | MC3

Question 5:MC4

Question 6:MC2 | MC4

Question 7:MC1

Question 8:MC2

Question 9:MC5

Question 10:MC2


Question 1:f(x) = 3x f(4) = 3(4) = 12

Question 2:f(x) = 5x + 4 f(6) = 5(6) + 4 = 34

Question 3:f(x) = 4x − 7 f(-3) = 4(-3) − 7 = -19

Question 4:

f(x) = x2 f(5) = (5)2 = 25 f(-5) = (-5)2 = 25

Question 5:f(x) = 2x f(5) = 2(5) = 10

Question 6:

f(x) = x3 f(2) = (2)3 = 8 f(-2) = (-2)3 = -8

Question 7:f(x) = 7x f(6) = 7(6) = 42

Question 8:

f(x) = 3⁄4 x f(4) = 3⁄4(4) = 3

Question 9:f(x) = 4x + 7 f(3) = 4(3) + 7 = 19

Question 10:

f(x) = 1⁄2 x + 1 f(2) = 1⁄2(2) + 1 = 2


Question 1:

f(x) = 10 + 7x + 5x2 f(2) = 10 + 7(2) + 5(2)2 f(2) = 10 + 7(2) + 5(4) f(2) = 10 + 14 + 20 f(2) = 44

Question 2:

f(x) = 12 + 10x − 5x2 f(-6) = 12 + 10(-6) − 5(-6)2 f(-6) = 12 + (-60) − 180 f(-6) = -228

Question 3:

f(x) = 18 + 9x − 3x2 f(3) = 18 + 9(3) − 3(3)2 f(3) = 18 + 27 − 27 f(3) = 18

Question 4:

f(x) = 12 + 3x − x2 f(5) = 12 + 3(5) − 52 f(5) = 12 + 15 − 25 f(5) = 2

Question 5:

f(x) = 9 + 3x + 6x2 f(-4) = 9 + 3(-4) + 6(-4)2 f(-4) = 9 + (-12) + 96 f(-4) = 93

Question 6:

f(x) = 17 − 7x + 2x2 f(7) = 17 − 7(7) + 2(7)2 f(7) = 17 − 49 + 98 f(7) = 66

Question 7:

f(x) = 3 + x + 4x2 f(9) = 3 + (9) + 4(9)2 f(9) = 3 + 9 + 324 f(9) = 336

Question 8:

f(x) = 4 + 4x − 4x2 f(2) = 4 + 4(2) − 4(2)2 f(2) = 4 + 8 − 16 f(2) = -4

Question 9:

f(x) = 15 + 4x − x2 f(5) = 15 + 4(5) − (5)2 f(5) = 15 + 20 − 25 f(5) = 10

Question 10:

f(x) = 10 + 2x + 3x2 f(6) = 10 + 2(6) + 3(6)2 f(6) = 10 + 12 + 108 f(6) = 130

Lesson Topic: Calculate functions word problems

Question 1:f(x) = 2.25 + 0.15x If x = 2, then f(x) = $2.55

Question 2:f(x) = 68 + 19.99x If f(x) = $207.93, then x = 7 months

Question 3:f(x) = 75 + 2x If x = 10, then f(x) = $95

Question 4:f(x) = 1.50 + 0.20x If f(x) = $1.90, then x = 2 refills

Question 5:If x = 4 , then f(x) = 4,800 ft

Question 6:Seven gift baskets were assembled, when six bottles of lotion are left.

f(x) = -2x + 206 = -2x + 20-14 = -2x7 = x

Question 7:f(x) = 50 + 35x If x = 18, then f(x) = $680

Question 8:f(x) = 3xIf x = 4, then f(x) = 12 years old

Question 9:f(x) = 0.95x + 1.65 If f(x) = $4.50, then x = 3 refills

Question 10:f(x) = 14.99x + 58 If x = 7 months, then f(x) = $162.93

Lesson Topic: Complete function tables

Question 1:5|1|2|23

Question 2:25|5|37|7

Question 3:1|9|4|25


Question 5:0|1|11|3


Question 7:0|1|8|10



Question 10:12|5|20|9

Lesson: Construct functions to model linear relationships

Lesson Topic: Identify rate of change from an equation in slope-intercept form

Question 1:The rate of change is m = -2


Question 3:

The rate of change is m = 1⁄4


Question 5:The rate of change is m = 9






Lesson Topic: Identify initial value or y-intercept from slope-intercept form

Question 1:The initial point of the function is b = 5

Question 2:The initial point of the function is b = -6


Question 4:

The initial point of the function is b = 12








Question 1:MC1

Question 2:MC5

Question 3:MC1

Question 4:MC1

Question 5:MC3

Question 6:MC5

Question 7:MC4

Question 8:MC3

Question 9:MC2

Question 10:MC5


Question 1:

When x = 0, y = 3 y = 1⁄2 x + 3

Question 2:

When x = 0, y = 4 y = 3⁄2 x + 4

Question 3:When x = 0, y = 1 y = 4x + 1

Question 4:

When x = 0, y = 2 y = 3⁄4 x + 2


Question 6:

When x = 0, y = 2 y = 1⁄3 x + 2



Question 9:

When x = 0, y = 6 y = 2⁄5 x + 6

Question 10:

When x = 0, y = 7 y = 2⁄3 x + 7


Question 1:

y = 1⁄2 x + b 4 = (1⁄2)(2) + b 4 = 1 + b 3 = b y = 1⁄2 x + 3

Question 2:

y = 3⁄2 x + b 7 = (3⁄2)(2) + b 7 = 3 + b 4 = b y = 3⁄2 x + 4

Question 3:y = 4x + b 5 = 4(1) + b 5 = 4 + b 1 = b y = 4x + 1

Question 4:

y = 3⁄4 x + b 5 = (3⁄4)(4) + b 5 = 3 + b 2 = b y = 3⁄4 x + 2


Question 6:y = 4x + b 10 = 4(1) + b 10= 4 + b 6 = b y = 4x + 6

Question 7:

y = 1⁄3 x + b 3 = (1⁄3)(3) + b 3 = 1 + b 2 = b y = 1⁄3 x + 2


Question 9:

y = 2⁄5 x + b 8 = (2⁄5)(5) + b 8 = 2 + b 6 = b y = 2⁄5 x + 6

Question 10:

y = 2⁄3 x + b 9 = (2⁄3)(3) + b 9 = 2 + b 7 = b y = 2⁄3 x + 7


Question 1:MC3

Question 2:MC1

Question 3:MC1

Question 4:MC4

Question 5:MC3

Question 6:MC1

Question 7:MC1

Question 8:MC4

Question 9:MC5

Question 10:MC5

Lesson Topic: Find a rate of change from a graph of a linear equation

Question 1:

m = 1⁄3

Question 2:

m = 1⁄4

Question 3:

m = -2⁄3

Question 4:

m = 4⁄4 = 1

Question 5:

m = -3⁄4

Question 6:

m = -2⁄2 = -1

Question 7:

m = -1⁄1 = -1

Question 8:

m = 6⁄1 = 6

Question 9:

m = 4⁄4 = 1

Question 10:

m = 3⁄2

Lesson Topic: Find the initial point from a graph of a linear equation

Question 1:The initial point, or y-intercept, is at (0, 3)

Question 2:The initial point, or y-intercept, is at (0, -1)









Lesson Topic: Derive functions from graphs

Question 1:MC4

Question 2:MC2

Question 3:MC3

Question 4:MC3

Question 5:MC3

Question 6:MC2

Question 7:MC3

Question 8:MC3

Question 9:MC2

Question 10:MC5

Lesson Topic: Complete a table to represent function values in a word problem

Question 1:6|12|18|24

Question 2:76|72|68|64

Question 3:8|10|12|14

Question 4:85|110|135|160

Question 5:90|86|82|78

Question 6:7|14|21|28

Question 7:20|40|60|80

Question 8:48|96|144|192

Question 9:55|80|105|130

Question 10:65|115|165|215

Defining functions Lesson Topic

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