2.3 Analyzing Graphs of Functions

A. Vertical Line Test (again)B. Domain and Range from a Graph

C. Zeros of a FunctionD. Intervals where Increasing, Decreasing, or Constant

A. Remember vertical line test?

• Here it is again:

B. Domain and Range from a Graph

• Break out the CRAYONS! Or just pretend.• For the DOMAIN of a graph, imagine a big

sunshine over and below it, casting a SHADOW onto the x-axis.

• The domain is usually written in interval notation.

State the domain in interval notation

Now for the Range (shadow on the y-axis)

Find the domain and range:

Find the domain and range:

C. If you’re asked to “find the zeros of the function,” it just means replace “f(x)” with zero and solve. Like

these:

5

32)(

10)(

103)(

2

2

t

tth

xxg

xxxf

D. Finding intervals where increasing, decreasing, or constant.

• “INCREASING” = “uphill from left to right”• “DECREASING” = “downhill from left to right”• “CONSTANT” = “horizontal”• “INCREASING” = positive slope• “DECREASING” = negative slope• “CONSTANT” = zero slope

ALL THESE INTERVALS ARE OPEN!

• WHEN ASKED TO FIND INTERVALS WHERE DECREASING,

INCREASING, CONSTANT, USE OPEN INTERVALS!

• ROUND BRACKETS, NOT SQUARE ONES.

State intervals where increasing, decreasing, or constant:

State intervals where increasing, decreasing, or constant:

State intervals where increasing, decreasing, or constant:

State intervals where increasing, decreasing, or constant: