Worksheet: Transformations of Graphs of Functions

In this worksheet, practice matching the graph of a function with its equation where x has been substituted with (x - h) and identifying even and odd functions from their graphs.

Q1:

The graph of function is produced from that of by the following steps: a shift of 4 to the right, a dilation by a scale factor of , and a shift of 4 up. What is the function ?

Q2:

Which of the following processes would you use to obtain the graph of from the graph of ?

reflect the graph in the -axis
reflect the graph in the -axis
reflect the graph in the line
reflect the graph in the line

Ab only
Ba only
Cc and d
Da and b
Ed only

Q3:

Given the graph of , which of the following is the graph of ?

Q4:

The following graph is a transformation of the graph of . What is the function it represents? Write your answer in a form related to the transformation.

Q5:

This is the graph of .

Which of the following is the graph of ?

A(c)
B(a)
C(b)

Q6:

Consider the following graph of the linear function .

Which of the following is the graph of the function ?

A(c)
B(a)
C(d)
D(b)

Q7:

This is the graph of the exponential function .

Which of the following is the graph of ?

A(c)
B(a)
C(b)

Q8:

On the left is the graph of and on the right is the graph of for some numbers and .

What is the pair ?

A
BThey cannot be determined.
C
D
E

Q9:

The graph of is given by the dashed red line in the following figure. Also shown are graphs of , , and . Match up these functions to their graphs.

A , ,
B , ,
C , ,
D , ,
E , ,

Q10:

The red graph in the figure has the equation and the blue graph has the equation . Express as a transformation of .

Q11:

Which of the graphs matches the equation ?