3.2, 3.3 - The graph of a function and properties of functions PDF

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The graph of a function and properties of functions...

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3.2 The graph of a Function Use the vertical line test. Example 1: Which graphs are graphs of a function?

Obtain Information From a Graph. Example 2:

a) Find F(-35) and f(-15)

g) What is the domain of f?

b) Find f(30) and f(0)

h) What is the range of f?

c) Is f (10) positive or negative?

i) What are the x-intercepts?

d) Is f(-35) positive or negative?

j) What are the y-intercepts?

e) For what value(s) of x is f(x)=0

k) How often does the line y=1 intersect the graph?

what values of x

0?

l) For what value(s) of x does f(x)=15?

Example 3 Determine whether the graph is that is of a function by using the vertical line test. a) What is the domain and range? b) What are the intercepts? c) Find any symmetry.

Example 4: a) b) c) d) e) f)

Is the point (-1, 2) on the graph of F? If x=4, what is f(x)? What point is on the graph of F? If f(x)=2, what is x? What point(s) are on the graph of f? What is the domain of f? List the x-intercepts, if any? List the y-intercepts, if any?

d) What is the domain of f? e) List the x-intercepts, if any? f) List the y-intercepts, if any?

3.3 Properties of Functions Determine Even and Odd Functions from a Graph

Even: y-axis symmetry Odd: origin symmetry Example 1

Is f strictly decreasing on the interval (2, 1)?

Identify Even and Odd Functions from the Equation Example 2

Use a Graph to Determine Where a Function is Increasing, Decreasing, or Constant Example 3 Determine where the function is increasing, decreasing, or constant. L epts, if any, and find the domain and range.

Use a Graph to Locate Local Maxima and Local Minima Example 4

Use a Graph to Locate the Absolute Maximum and the Absolute Minimum

Find the Average Rate of Change

Example 5 Find the average rate of change of a) From 1 to 3 b) From 1 to 5

c) From 1 to 7...