# 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 ?

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**Q2: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

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**Q3: **

The figure shows the graph of .

Which of the following is the graph of ?

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**Q4: **

The figure shows the graph of .

Which of the following is the graph of ?

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**Q6: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

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**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.

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**Q12: **

The red graph in the figure represents the equation and the purple graph represents the equation . Express as a transformation of .

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**Q13: **

The red graph in the figure represents the equation and the orange graph represents the equation . Express as a transformation of .

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**Q14: **

The figure shows the graph of and the point . The point is a local maximum. Identify the corresponding local maximum for the transformation .

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**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 .

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**Q17: **

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

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**Q18: **

The figure shows the graph of .

Which of the following is the graph of ?

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**Q19: **

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

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**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 .

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

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**Q21: **

Consider the function .

Which of the following is the graph of ?

- AD
- 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 .

- Adomain: , range:
- Bdomain: , range:
- Cdomain: , range:

**Q22: **

The figure shows the graph of .

Which of the following is the graph of ?

- A
- B
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- E

**Q23: **

This is the graph of .

Which of the following is the graph of ?

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