Question 1

Which of the following describes the effect of multiplying the function $$f(x) = \sqrt{x} by a $$constant $$a \u003e 1$$?

Accepted Answer

It stretches the graph vertically by a factor of $$a.$$

Question 2

Given $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = |x| + 2$$?

Accepted Answer

It shifts the graph of $$f(x)$$ upward by 2 units.

Question 3

If $$h(x) = \sqrt{x}$$ and $$k(x) = \frac{1}{2}\sqrt{x}$$, which statement best describes the transformation from $$h(x) to$$ $$k(x)$$?

Accepted Answer

The graph of $$h(x) is $$shrunk vertically by a factor of $$\frac{1}{2}.$$

Question 4

Suppose $$f(x) = \sqrt{x}$$ and $$g(x) = \sqrt{x} + 3. $$What is the $$y-$$intercept of $$g(x)$$?

Accepted Answer

$$3$$

Question 5

Which transformation will shift the graph of $$f(x) = |x|$$ downward by 2 units?

Accepted Answer

$$g(x) = |x| - 2$$

Question 6

If $$f(x) = \sqrt{x}$$, which of the following represents a vertical stretch by a factor of $$3$$ and a shift upward by $$2$$ units?

Accepted Answer

$$g(x) = 3\sqrt{x} + 2$$

Question 7

A medical researcher models the recovery rate of a drug with $$f(x) = \sqrt{x}$$, where $$x is $$the number of days since treatment. If the recovery rate is observed to be half as fast, which function best models the new recovery rate?

Accepted Answer

$$g(x) = \frac{1}{2}\sqrt{x}$$

Question 8

Which of the following transformations will reflect the graph of $$f(x) = \sqrt{x}$$ across the $$x-$$axis?

Accepted Answer

$$g(x) = -\sqrt{x}$$

Question 9

If $$f(x) = |x|$$, which transformation results in a graph that is both vertically stretched by a factor of $$2$$ and shifted downward by $$3$$ units?

Accepted Answer

$$g(x) = 2|x| - 3$$

Question 10

A company models its profit with $$f(x) = |x|$$, where $$x is $$the number of products sold. If the company increases its base profit by $$5$$ units, which function models the new profit?

Accepted Answer

$$g(x) = |x| + 5$$

Question 11

Given $$f(x) = \sqrt{x}$$, which transformation will shrink the graph vertically by a factor of $$\frac{1}{4}$$ and shift it upward by $$1$$ unit?

Accepted Answer

$$g(x) = \frac{1}{4}\sqrt{x} + 1$$

Question 12

If $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = |x| - 2$$?

Accepted Answer

It shifts the graph of $$f(x)$$ downward by 2 units.

Question 13

Which of the following best describes the transformation from $$f(x) = \sqrt{x} to$$ $$g(x) = \sqrt{x} - 2$$?

Accepted Answer

The graph is shifted downward by 2 units.

Question 14

A scientist models the growth of bacteria with $$f(x) = \sqrt{x}$$, where $$x is $$time in hours. If the bacteria grow twice as fast, which function best models the new growth?

Accepted Answer

$$g(x) = 2\sqrt{x}$$

Question 15

If $$f(x) = |x|$$, which transformation will reflect the graph across the $$x-$$axis?

Accepted Answer

$$g(x) = -|x|$$

Question 16

Which of the following transformations will shift the graph of $$f(x) = \sqrt{x}$$ upward by $$4$$ units?

Accepted Answer

$$g(x) = \sqrt{x} + 4$$

Question 17

If $$f(x) = |x|$$, which transformation will shrink the graph vertically by a factor of $$\frac{1}{3}$$?

Accepted Answer

$$g(x) = \frac{1}{3}|x|$$

Question 18

A student graphs $$f(x) = \sqrt{x}$$ and $$g(x) = \sqrt{x} + k. If$$ $$k \u003c 0$$, what happens to the graph of $$f(x)$$?

Accepted Answer

It is shifted downward by $$|k|$$ units.

Question 19

Which transformation will both reflect the graph of $$f(x) = \sqrt{x}$$ across the $$x-$$axis and shift it upward by $$3$$ units?

Accepted Answer

$$g(x) = -\sqrt{x} + 3$$

Transformations of Functions: Stretching, Shrinking, and Vertical Translation

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