Chapter 1 Notes

Chapter 1 NotesSection 1.3

Graphs of Functions

Graphs of functions are the collections of ___________________

Where x is the ___________of the function, also called the __________ of the function f

And f(x) is the ____________of the function (y-value)

1.3 Notes (continued)• A graph of function f is

shown• Use the picture of f to

determine the domain ______

• Use the picture to determine the range ______

• Use the picture to findf(2) _____f(0) _____f(-1) _____f(4) _____

1.3 Notes (continued)• Finding Domain and range of a function• If• What is the domain?

• What is the range?

• Check your result graphically

1 xxf

1.3 Notes (continued)• Testing of Graphs for Functions• Use the Vertical Line Test

VLT –

Which of the following graphs are functions?

1.3 Notes (continued)• Increasing, Decreasing, or Constant

– A function is __________ on an interval if, for any x1

and x2, in the interval, ________________________– A function is __________on an interval if, for any x1 and x2, in the interval, ________________________– A function is ________ on an interval if, for any x1 and x2, in the interval, __________________– In other words

• Increasing – ____________________• Decreasing – ___________________• Constant – __________________

1.3 Notes (continued)• Shown to the right is

a graph of a function f.

• On what interval(s) is f increasing, decreasing, and/or constant?

• Increasing• Decreasing• Constant

_______ ____________ ______________ _______

f x

1.3 Notes (continued)• Shown to the right is

a graph of a function f(x) = x3-3x

• On what interval(s) is f increasing, decreasing, and/or constant?

• Increasing ______• Decreasing ______• Constant ______

1.3 Notes (continued)Minimums and Maximums

A function’s value f(a) is a called a _________________ of f if there exists an interval (x1,x2) that contains a such that ____________________

A function’s value f(a) is called a ________________of f if there exists an interval (x1,x2) that contains a such that ____________________

1x 2x

xfaf

a

1.3 Notes (continued)• In General, a function can have any

number of relative mins/maxs

• Some functions may have what is called an ABSOLUTE maximum or minimum– Where that particular value of the function is

the maximum or minimum over the entire domain of the function.

1.3 notes (continued)• Finding relative mins/maxs using calculator.• Approximate any relative minimums or

maximums of

64

22

23

xxxh

xxxxf

1.3 Notes (continued)• Sketching a Piecewise graph by hand.

15212

xxxx

xf

1.3 Notes (continued)• Even, Odd, or Neither.• A function is said to be an ________Function if

• Even functions are symmetric about the y-axis• Or, each value of x and it’s opposite (-x) give the

same value of the function.• A function is said to be an ________ Function if

• Odd functions are symmetric about the origin• Or, each value of x and it’s opposite (-x) give the

opposite value of the function.

______ ______

______ ______

1.3 Notes (continued)• Is f(x) even, odd or neither?

• So, • Graphically -

2 4f x x

1.3 Notes (continued)• Is g(x) even, odd or neither?

• So, • Graphically -

3g x x x