Question 1

Suppose the function $$f(x)$$ represents the height (in meters) of a ball thrown upward, where $$f(x) = -5x^2$ + 20x + 2. If $$the function is transformed to $$g(x) = f(x-3) + 4$$, which of the following best describes the transformation applied to the graph of $$f(x)$$?

Accepted Answer

Shifted 3 units to the right and 4 units upward

Question 2

Given $$f(x) = \sqrt{x}$$, which transformation results in the graph of $$y = -2f(x+1)$$?

Accepted Answer

Reflect about the x-axis, stretch vertically by a factor of 2, and shift left by 1 unit

Question 3

A population model is given by $$f(x) = 100e$$^{0.05x}$$. If the function is transformed to g(x) = f(2x$$)$$, what effect does this have on the graph?

Accepted Answer

The graph is horizontally shrunk by a factor of 2

Question 4

If $$f(x) is a $$function and $$g(x) = f(-x)$$, which transformation is represented?

Accepted Answer

Reflection about the y-axis

Question 5

The graph of $$y = f(x) is $$reflected about the x-axis and then shifted downward by 5 units. Which equation represents this transformation?

Accepted Answer

$$y = -f(x) - 5$$

Question 6

A company’s profit function is $$f(x). If $$the graph of $$y = f(x) is $$vertically shrunk by a factor of $$\frac{1}{3}$$, which equation represents the new profit function?

Accepted Answer

$$y = \frac{1}{3}f(x)$$

Question 7

Given $$f(x) = x^2$, which transformation results in the graph of y = f(x+2) - 7$?

Accepted Answer

Shift left by 2 units and down by 7 units

Question 8

If $$f(x)$$ models the temperature in a chemical reaction over time, and $$g(x) = 4f(x)$$, what does this transformation represent?

Accepted Answer

The temperature values are quadrupled (vertical stretch by 4)

Question 9

Which of the following correctly describes the order in which transformations should be applied to a function?

Accepted Answer

Horizontal shifting, stretching/shrinking, reflection, vertical shifting

Question 10

A medical dosage function is $$f(x). If $$the graph is reflected about the y-axis and then shifted 2 units to the right, which equation represents the transformation?

Accepted Answer

$$y = f(-x+2)$$

Question 11

Given $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = f(x-4)$$?

Accepted Answer

Shift the graph 4 units to the right

Question 12

If $$f(x) is a $$function and $$g(x) = f(-x) + 3$$, which sequence of transformations is applied to $$f(x)$$?

Accepted Answer

Reflect about the y-axis, then shift up by 3 units

Question 13

A function $$f(x) is $$horizontally stretched by a factor of 5. Which equation represents this transformation?

Accepted Answer

$$y = f\left(\frac{1}{5}x\right)$$

Question 14

Suppose $$f(x) is $$the cost function for producing $$x$$ units of a product. If the graph is reflected about the x-axis and then stretched vertically by a factor of 2, which equation represents the new cost function?

Accepted Answer

$$y = -2f(x)$$

Question 15

Given $$f(x) = x^3$, what is the effect of the transformation g(x) = f(-x$$)$$?

Accepted Answer

Reflection about the y-axis

Question 16

A function $$f(x) is $$transformed to $$g(x) = f(x) + 8. $$What is the effect on the graph?

Accepted Answer

Shift the graph 8 units upward

Question 17

If $$f(x) is a $$function and $$g(x) = f(x+5)$$, what is the effect on the graph of $$f(x)$$?

Accepted Answer

Shift the graph 5 units to the left

Question 18

A function $$f(x) is $$vertically stretched by a factor of $$\frac{1}{2}$$ and then shifted down by 3 units. Which equation represents this transformation?

Accepted Answer

$$y = \frac{1}{2}f(x) - 3$$

Question 19

Given $$f(x) = x^2$, which transformation results in the graph of y = -f(x-2$$)$$?

Accepted Answer

Reflect about the x-axis and shift right by 2 units

Transformations of Functions: A Precalculus Study Guide

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