Lesson 1.3

Read: Pages 42-47

Page 38: #1-49 (EOO), #61-85 (EOO)

Graph of Functions

Objective

Students will know how to analyze graphs of functions.

 

Domain - set of input values.

Range - set of output values.

Function - is a relation that has exactly one output for each input.

“one y value for every x value”

Illustration of Domain and Range

Use the graph of the function to find the domain and range of f. Then find f(0).

Find the domain and range of the function algebraically.

   

Vertical Line Test

A relation is a function if and only if no vertical line intersects the graph of the

relation at more than one point.

Vertical Line Test

y

x

y

x

Function Not a Function

Use the Vertical Line Test to determine whether y is a function of x.

12 yx 122 xyx

Increasing, Decreasing and Constant Functions

Determine the open intervals over which the function is increasing, decreasing, or constant.

   

Definitions of Relative Minimum and Relative Maximum

Approximate any relative minimum or relative maximum values of the function. (Graph the function)

 

Sketch the graph of the piecewise-defined function by hand.

 

 

Symmetric Graphs

Graphically determine whether the function is even, odd, or neither. Verify your answer algebraically.

   

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and

the function is (a) even and (b) odd.

(5,-1)