# Worksheet: Function Transformations: Translations

In this worksheet, we will practice identifying function transformations involving horizontal and vertical shifts.

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:

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

Q3:

This is the graph of . Which of the following is the graph of ?  • A(c)
• B(b)
• C(a)

Q4:

Consider the following graph of the linear function . Which of the following is the graph of the function ? • A(d)
• B(a)
• C(b)
• D(c)

Q5:

Which of the following is the graph of ?  • A(c)
• B(d)
• C(a)
• D(b)

Q6:

Which function is represented below? • A
• B
• C
• D
• E

Q7:

The function is translated 2 units in the direction of the positive x-axis. What is the equation of the resulting function?

• A
• B
• C

Q8:

This is the graph of the exponential function . Which of the following is the graph of ?  • A(a)
• B(b)
• C(c)

Q9:

The function is stretched in the horizontal direction by a scale factor of and in the vertical direction by a scale factor of . Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q10:

The function is translated eight down. Write, in terms of , the equation of the translated graph.

• A
• B
• C
• D
• E

Q11:

The function is stretched in the horizontal direction by a scale factor of 2 and in the vertical direction by a scale factor of 2. Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q12:

The function is stretched in the horizontal direction by a scale factor of . Write, in terms of , the equation of the transformed function.

• A
• B
• C
• D
• E

Q13:

Daniel thinks that he can map the graph of the function to the graph of any other linear function by a translation followed by a stretch. This is equivalent to saying that any linear function can be written in the form for suitable values of and .

Is he right?

• Ano
• Byes

Suppose that and is as before. Find and in terms of and when it is possible to write in the form .

• A,
• B,
• C,
• D,
• E,

Let and . Find the values of and for which . Use the following graph to help you. • A,
• B,
• C,
• D,
• E,

Q14:

Consider the function .

Which of the following is the graph of ? • AC
• BB
• CA
• DD

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:

Q15:

Consider the function .

Which of the following is the graph of ? • BC
• CB
• DA

How would you describe the transformation from to ?

• Atranslation three units up
• Bdilation in the horizontal direction by a factor of 3
• Cdilation in the vertical direction by a factor of 3

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:

Q16:

Consider the function given by .

The function is obtained by dilating in the horizontal direction by a factor and translating it units horizontally. Write the equation for .

• A
• B
• C
• D

Find so that .

• A
• B
• C
• D

Find so that .

• A
• B
• C
• D

Use your previous answers to find the equation of the graph shown in the given diagram. • A
• B
• C
• D

Q17:

Consider the root function .

The function has been obtained by translating three units down and five units to the left. Write its equation.

• A
• B
• C
• D
• E

State the domain and range of .

• Bdomain: , range:
• Cdomain: , range:
• Ddomain: , range:
• Edomain: , range:

Q18:

Consider the function given by .

The function is obtained by dilating in the vertical direction by a factor and translating it units horizontally and units vertically. Write an equation for .

• A
• B
• C
• D

Where is the origin mapped to when transforming from the graph of to the graph of ?

• A
• B
• C
• D

Find .

• A
• B
• C
• D

Use your previous answers to find the equation of the graph shown in the given diagram. • A
• B
• C
• D

Q19:

This is the graph of . Which of the following is the graph of ?  • A(c)
• B(a)
• C(b)

Q20:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q21:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q22:

The red graph in the figure has equation and the black graph has equation . Express as a transformation of . • A
• B
• C
• D
• E

Q23:

The figure shows the graph of and point . Point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q24:

The figure shows the graph of and point , which is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E

Q25:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A
• B
• C
• D
• E