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 .
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Q3:
The figure shows the graph of .
Which of the following is the graph of ?
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- E
Q4:
The figure shows the graph of .
Which of the following is the graph of ?
- A
- B
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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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- 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 .
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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 ?
- A
- B
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- D
- E
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
- C
- D
- E
Q23:
This is the graph of .
Which of the following is the graph of ?
- A(c)
- B(a)
- C(b)