Question 1

Which of the following equations represents a vertical shift of the parent function $$f(x) = x^2$ up by 4 units?

Accepted Answer

$$f(x) = x^2$ + 4$$

Question 2

Given the function $$g(x) = |x - 3|$$, which transformation has been applied to the parent function $$f(x) = |x|$$?

Accepted Answer

A horizontal shift right by 3 units

Question 3

If $$h(x) = -2\sqrt{x}$$, which of the following best describes the transformation(s) from the parent function $$f(x) = \sqrt{x}$$?

Accepted Answer

Reflection over the x-axis and vertical stretch by a factor of 2

Question 4

A city’s average water consumption is modeled by $$W(t)$$, peaking at 180 units in summer. Next year, due to drought, usage will be 25 units higher at every point. Which function models next year’s usage?

Accepted Answer

$$W_{next}(t) = W(t) + 25$$

Question 5

Given $$f(x) = (x + 2)^2$ - 5$$, what is the sequence of transformations applied to $$f(x) = x^2$?

Accepted Answer

Shift left 2 units, shift down 5 units

Question 6

An audiologist finds that a patient’s hearing threshold is modeled by $$S(f) = H(f - 500)$$, where $$H(f) is $$the healthy curve. What does this transformation mean?

Accepted Answer

The patient hears each frequency as if it were 500 Hz lower

Question 7

If $$f(x) = x^3$, which function represents a vertical stretch by a factor of 3 and a shift up by 2 units?

Accepted Answer

$$g(x) = 3x^3$ + 2$$

Question 8

A muscle force function for an athlete is $$u(v) = 1.8f(v)$$, where $$f(v) is $$the untrained force. If the untrained force at $$v = 2 is 200 N$$, what is the athlete’s force?

Accepted Answer

360 N

Question 9

Which of the following is the parent function for the supply function $$P = \frac{2}{3}Q$$?

Accepted Answer

$$P = Q$$

Question 10

Given $$f(x) = |x|$$, which function represents a reflection over the x-axis and a shift right by 2 units?

Accepted Answer

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

Question 11

If $$f(x) = \sqrt{x}$$, which transformation results in $$g(x) = \sqrt{x - 4} + 3$$?

Accepted Answer

Shift right 4 units, shift up 3 units

Question 12

A second athlete can only exert 60% of their normal force. If $$u(v) is $$the normal force, which function models the injured athlete’s force?

Accepted Answer

$$c(v) = 0.6u(v)$$

Question 13

Given the demand function $$P = \frac{4000}{Q} - 40$$, what is the parent function and the transformation?

Accepted Answer

Parent: $$P = \frac{1}{Q}$$; vertical stretch by 4000 and shift down by 40

Question 14

Which transformation is applied to $$f(x) = x^2$ to obtain g(x) = -(x$$ - $$1)^2 + 3$?

Accepted Answer

Reflect over x-axis, shift right 1 unit, shift up 3 units

Question 15

If $$f(x) = x^3$, which function represents a horizontal shift left by 2 units?

Accepted Answer

$$g(x) = (x + 2)^3$

Study Guide: Transformations of Graphs in College Algebra

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