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Worksheet: Transformations of Graphs of Functions

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 ?

  • A
  • B
  • C
  • D
  • E

Q2:

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

  1. reflect the graph in the -axis
  2. reflect the graph in the -axis
  3. reflect the graph in the line
  4. reflect the graph in the line
  • Ad only
  • Bc and d
  • Ca and b
  • Db only
  • Ea only

Q3:

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

  • A
  • B
  • C
  • D

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.

  • A
  • B
  • C
  • D
  • E

Q5:

This is the graph of .

Which of the following is the graph of ?

  • A(b)
  • B(c)
  • C(a)

Q6:

Consider the following graph of the linear function .

Which of the following is the graph of the function ?

  • A(d)
  • B(b)
  • C(c)
  • D(a)

Q7:

This is the graph of the exponential function .

Which of the following is the graph of ?

  • A(b)
  • B(c)
  • C(a)

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
  • B
  • C
  • D
  • EThey cannot be determined.

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 .

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the graphs matches the equation ?