# Lesson Worksheet: Function Transformations: Dilation Mathematics

In this worksheet, we will practice identifying function transformations involving horizontal and vertical stretches or compressions.

Q1:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q2:

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

Q3:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q4:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q5:

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

Q6:

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

Q7:

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

• A
• B
• C
• D
• E

Q8:

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

• A
• B
• C
• D
• E

Q9:

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation . • A(1,1)
• B(4,2)
• C(2,1)
• D(4,1)
• E

Q10:

The function is stretched 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

Q11:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q12:

The red graph in the figure represents the equation and the purple graph represents the equation . Express as a transformation of . • A
• B
• C
• D

Q13:

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

Q14:

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

Q15:

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

Q16:

A car factory manufactures a different number of cars every month based on a certain function . In a certain year, the factory manager decided to increase the monthly rate by a factor of 2 based on a function . Find in terms of .

• A
• B
• C
• D
• E

Q17:

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

Q18:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q19:

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

Q20:

The graphs of three square root functions are shown in the given diagram. The equations for curves A and B have the form for some integers and . Curve C can be obtained by dilating curve B in the vertical direction. Write the corresponding equation for curve C in the form .

• A
• B
• C
• D
• E

Curve C can also be obtained by dilating curve A in the horizontal direction. Write the corresponding equation for curve C in the form .

• A
• B
• C
• D
• E

Q21:

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:

Q22:

The figure shows the graph of . Which of the following is the graph of ?

• A • B • C • D • E Q23:

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

Q24:

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

Q25:

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 (a), (b), (c)
• B (a), (c), (b)
• C (c), (b), (a)
• D (c), (a), (b)
• E (b), (c), (a)