nelsonamy101.files.wordpress.com …  · Web viewThe Gomez family is traveling at a rate of 70 miles per out. The function rule that represents this situation is 70x, where x is

Course 1 Unit 8Functions and Inequalities

Name: ___________________Lesson 8-1: Function Tables

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function– _________________________________________________________________________________________________________________________________________________________________________________________function rule – __________________________________________________________________________________________________________________________________________________________________________________function table – __________________________________________________________________________________________________________________________________________________________________________________independent variable – _______________________________________________________________________dependent variable – __________________________________________________________________________Example 1The output is 7 more than the input. Complete a function table for this relation.Input (x) x + 7 Output (y)101214

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Example 2The output is 5 times the input. Complete a function table for this relation.Input (x) 5x Output (y)81012

Got it? 1. Input (x) x - 4 Output (y)4710

2. Input (x) 3x Output (y)025

Example 3Find the input for the function table.Input (x) 3x Output (y)~ 3 ~

61521Got it? 3) Input (x) 3x Output (y)0254. Input (x) 3x Output (y)172029Example 4The Gomez family is traveling at a rate of 70 miles per out. The function rule that represents this situation is 70x, where x is the number of hours. Make a table to find out how many hours they have driven at 140 miles, 280 miles, and 350 miles. Then graph the function.First find the input values for x. Input (x) 70x Output (y)70 ⋅ _____ 14070 ⋅ _____ 28070 ⋅ _____ 350Then plot each ordered pair on the graph.

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0 1 2 3 4 50

100

200

300

400

500

Got it? 5) Eva bikes 12 miles per hour. The function rule that represents this situation is 12x, where x is the number of hours. Make a table to find how many hours she has biked when she has gone 12, 36, and 48 miles. Then graph the function.Input (x) 12x Output (y)12 ⋅ _____ 1212 ⋅ _____ 3612 ⋅ _____ 48Guided Practice:1. Isaiah is buying jelly beans. In bulk, they costs $3 per pound, and a candy dish cost $2. The function rule, 3x + 2 where x is the number of pounds, can be used to find the total cost of x pounds of jelly beans in 1 dish. Make a table that shows the total cost of buying 2, 3, or 4 pounds of jelly beans and 1 dish.

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2. Jasper hikes 4 miles per hour. The function rule that represents this situation is 4x. Make a table to find how many hours he has hiked in 8, 12, and 20 miles. Then graph the function.

Lesson 8-2 Function Rulessequence – _____________________________________________________________________________________term – __________________________________________________________________________________________arithmetic sequence – _________________________________________________________________________geometric sequence – _________________________________________________________________________

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Example 1Describe the relationship between the terms in the arithmetic sequence 7, 14, 21, 28, … Then write the next three terms.7, 14, 21, 28, …Each term is found by adding ________ to the previous term.28 + 7 = ________35 + 7 =________42 + 7 = ________The next three terms are ________, ________, and ________.Example 2Describe the relationship between the terms in the geometric sequence 2, 4, 8, 16, … Then write the next three terms.2, 4, 8, 16, …Each term is found by multiplying the previous term by ________.The next three terms are ________, ________, and ________.Got it? Find the pattern in each sequence. Then find the next three terms.1) 0, 15, 30, 45, … 2) 4.5, 4, 3.5, 3, …

3) 1, 3, 9, 27, … 4) 3, 6, 12, 24, …Example 3Use words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term.

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What is the function rule?Each number is 3 times its position number.So the function rule is _______.The value of the tenth term is ______________. Got it? Use words and symbols to describe the value of each term as a function of its position. Then find the value of the eighth term.5) 6)

Example 4The table shows the number of necklaces Hannah can make, based on the number of hours she works. Write a function rule to find the number of necklaces she can make in x hours.

Notice the values 5, 7, 9, … increase by 2, so the rule includes 2x.If it were simply 2x, then the number in 1 hour would be 2, but it is 5, which is 3 more. So the rule is ________________. Got it? 7) The table shows the fee for overdue books at a library, based on the number of weeks the book is overdue. Write a function rule to find the fee for a book that is x weeks overdue.

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Guided Practice: 1. Describe the relationship between the terms in the sequence 13, 26, 52, 104,… Then write the next three terms.

2. Use words and symbols (expression) to describe the value of each term as a function to the position. Then find the value of the fifteenth term in the sequence.

3. What is the difference between an algebraic and geometric sequence?

Lesson 8-3: Functions and Equations~ 9 ~

linear function – ______________________________________________________________________________Example 1Write an equation to represent the function shown in the table.

The value of y is equal to 9 times the value of x. So, the equation that represents the function is _________________. Got it? 1) Write an equation to represent the function shown in the table.

Example 2:Graph y = 2x.Step 1: Make a table of ordered pairs. Select “nice” numbers for x. Substitute these values for x to find y.

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Step 2: Graph each ordered pair. Draw a line through each point.

Got it? Graph each equation.2) y = x + 1 3. y = 3x + 2

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Example 3Adrian constructed the graph shown, which shows the height of his cactus after several years of growth.

Make a function table for the input-output values.

The input values are 1, 2, and 3 and the output values are 42, 44, and 46.Example 4Write an equation from the graph that could be used to find the height y of the cactus after x years (refer to Example 3).Since the values increase by 2, the equation includes ______x.

The output value for 1 is 42. 2(1) = 2 so 42 is _________ more than that.So the equation is y = 2x + _________.Got it? 4) The graph shows the total amount y that you spend if you buy one book and x magazines. Make a function table for the input-output values.

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5) Write an equation from the graph that could be used to find the total amount y if you buy one book and x magazines.

Guided Practice:1. Write an equation to represent the function shown in the table.

2. Graph the function y = x + 3.

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3. The graph below shows the number of inches of rainfall x equivalent to inches of snow y. Make function table for the input-output values. Write an equation from the graph that can be used to find the total inches of snow y equivalent to inches of rain x.

Equation: ____________________________Lesson 8-4 Multiple Representations of FunctionsExample 1The drama club is holding a bake sale. They are charging $5 for each pie they sell. Write an equation to find the total amount earned t for selling p pies. Words: Total earned _______________ $5 ___________ the number of _________ soldVariable: t = total; p = piesEquation: ___________________Example 2In a science report, Alexis finds that the average adult breathes 14 times each minute when not active. Write an equation to find the total breaths b a non-active person takes in m minutes.b = breaths; m = minutes

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Total breaths equals __________ times the number of _________________Equation: ____________________Got it? 1) A mouse can travel 8 miles per hour. Write an equation to find the total distance d a mouse can travel in h hours.

2) Natalie can make 36 cookies each hour. Write an equation to find the total number of cookies c that she can make in h hours.Example 3The Student Council is holding a car wash to raise money. They are charging $7 for each car they wash.Write an equation and make a function table to show the relationship between the number of cars washed c and the total amount earned t.

Equation: ____________________________Got it? While in normal flight, a bald eagle flies at an average speed of 30 miles per hour.

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3) Write an equation and make a function table to show the relationship between the total distance d that a bald eagle can travel in h hours.4) Graph the ordered pairs of the function. Analyze the graph.

Guided Practice:1. The school cafeteria sells lunch passes that allow a student to purchase any number of lunches in advance for $3 a lunch. a. Write an equation for this situation.Equation: _______________________________________b. Make a table.

c. Graph the ordered pairs.~ 16 ~

d. Analyze the graph.

Lesson 8-5: Inequalitiesinverse operations – _________________________________________________________________________inequality – ___________________________________________________________________________________Symbols:Symbols < > ≤ ≥Words Is less than

Is fewer than Is greater than Is more

Is less than or equal to Is greater than or equal to

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than Is at most Is at leastExampleExample 1Of the numbers 6, 7, or 8, which is a solution of the inequality f + 2 ¿ 9?Replace f with the numbers: (Circle the one that is true)6 + 2 = 87 + 2 = 98 + 2 = 10Got it? 1) Of the numbers 8, 9, or 10, which is a solution of the inequality n – 3 ¿ 6?Example 2Is the given value a solution of the inequality?x + 3 ¿ 9, x = 4

________ + 3 = __________________ is not greater than 9, so __________ 4 is not a solution.Example 3Is the given value a solution of the inequality?12 ≤ 18 – y, y = 6

_________ – 6 = _________Since 12 = 12, ______________6 is a solution.

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Example 4: Is the given value a solution of the inequality?17 ≥ 11 + x, x = 811 + ___________ = ____________

_____________ is not greater than or equal to 19, so ____________ 8 is not a solution.Got it? Is the given value a solution of the inequality?2) a + 7 ¿ 15, a = 9

3) 22 ≤ 15 + b, b = 6

4) 12 ≥ 5 + g, g = 7

Example 5Kendall works at a gift shop. She receives a bonus if she makes more than 20 balloon bouquets in a month. Which months did Kendall receive a bonus? Use the inequality b ¿ 20, where b represents the number of balloon bouquets made each month, to solve.

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Answer: ____________________ and _____________________Got it? 5) If the bakery sells more than 45 bagels in a day, they make a profit. Use the inequality b ¿ 45 to determine which days the bakery made a profit.

Equations vs. Inequalities EQUATIONS INEQUALTIESEXAMPLE

NUMBER OF SOLUTIONSGuided Practice:Determine which number is a solution of the inequality.1. 9 + a < 17; 7, 8, 9 2. b – 10 > 5; 14, 15, 16

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Is the given value a solution of the inequality? 3. x – 5 < 5, x = 15 4. 32 ≥ 8n; n = 3

5. If the bakery sells more than 45 bagels in a day, they make a profit. Use the inequality b > 45 to determine which days the bakery makes a profit. Day Number of Bagels SoldMonday 18Tuesday 25Wednesday 21Thursday 36Friday 50Saturday 48Sunday 40

6. What is the difference in the number of solutions between an equation and an inequality?

Lesson 8-6: Write and Graph Inequalities~ 21 ~

Example 1Write an inequality for the sentence.You must be over 12 years old to ride the go-karts.Variable: let a = your ageWords: your age is over 12Inequality: __________________________Example 2Write an inequality for the sentence.A pony less than 14.2 hands tall.Variable: p = height of the ponyWords: A pony is less than 14.2Inequality: ______________________________Example 3Write an inequality for the sentence.You must be at least 16 years old to have a driver’s license.Variable: let a = your ageWords: your age is at least 16 yearsInequality: ______________________________________Got it? Write an inequality for each situation.

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1) You must be older than 13 to play in the basketball league.

2) To use one stamp, your letter must weigh under 3.5 ounces.

3) You must be at least 18 years old to vote.Example 4Graph the inequality on a number line. n ¿9Make a number line. Place an open dot at 9. Then draw a line and an arrow to the right.

Example 5Graph the inequality on a number line. n ≤ 10Make a number line. Place a closed dot at 10. Then draw a line and an arrow to the left.Got it? Graph each inequality on a number line.4) a ¿ 15

5) b ≥ 7Example 6

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Traffic on a residential street can travel at speeds of no more than 25 miles per hour. Write and graph an inequality to describe the possible speeds on the street.Let s represent the speed. s ≤ 25Got it? 6) Tasha can spend no more than $40 on new boots. Write and graph an inequality to describe how much she can spend.

Guided Practice:Write an inequality for each sentence. 1. The movie will be no more than 90 minutes in length.2. The mountain is at least 985 feet tall. Graph each inequality on a number line.3. a ≤ 6 4. b > 4

5. Give an example of an inequality where you would draw an open dot when graphing.

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Lesson 8-7 Solve One-Step InequalitiesExample 1Solve x + 7 ≥ 10. Graph the solution on a number line.Use inverse operations.x + 7≥ 10 - 7 - 7 x ≥ 3 The solution is x ≥ _________.To graph it, draw a closed dot at 3 and draw an arrow to the right on the number line. (Graph below)

Example 2Solve x – 3 ¿ 9. Graph the solution on the number line. Use inverse operations. x – 3 ¿ 9 + 3 +3 x ¿ 12 The solution is x ¿ ___________. To graph it, draw an open dot on 12 and draw an arrow to the left of the number line. (Graph below)

Got it? Solve and graph the inequality.1) n + 2 ≤ 5 2) y – 3 ¿9Example 3Solve 5x ≤ 45. Graph the solution on a number line. (Graph below)

5x ≤ 455x5 ≤ 455

x ≤ _________~ 25 ~

Example 4Solve x8 ¿ 3. Graph the solution on a number line. (Graph below)x8 ¿ 3

x8 (8) ¿ 3 (8)

x ¿ __________Got it?Solve and graph the inequality.3) 10x ¿ 80 4) x6 ≥ 7Example 5Drew is making bags of party favors for each of the 7 friends attending his birthday party. He does not want to spend more than $42 on the party favors. Write and solve an inequality to find the maximum cost for each party favor bag.Let c represent the cost for each bag of party favors.

7 times the cost of each bag must be no more than $42.7c ≤ 427c7 ≤ 427c ≤ $6So Drew can spend a maximum of $___________ on each bag.

Guided PracticeSolve each inequality. Make a number line and graph the solution. 1. h – 6 ≥ 13 2. 5y > 30

3. Tino’s Pizza charges $9 for a cheese pizza. Eileen has $45 to buy pizza for the Spanish Club. Write and solve an inequality to find the maximum number of pizzas that Eileen can buy. ~ 26 ~

4. How is solving an equation similar to solving an inequality?

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