Question 1

Which of the following best describes the transformation from the graph of $$y = |x| to $$the graph of $$y = |x| + 4$$?

Accepted Answer

A vertical shift upward by 4 units

Question 2

Given the function $$f(x) = x^2$, what is the equation of the function whose graph is the graph of f(x$$)$$ shifted 3 units to the right and 2 units down?

Accepted Answer

$$y = (x - 3)^2$ - 2$$

Question 3

Which of the following describes the transformation from $$y = x^3$ to y$$ = $$-x^3$$?

Accepted Answer

Reflection in the x-axis

Question 4

Evaluate the cube root function $$p(x) = \sqrt[3]{x} at$$ $$x = -27.$$

Accepted Answer

$$-3$$

Question 5

Which of the following is the domain of the square root function $$n(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 6

If $$y = 2|x|$$, how does its graph compare to $$y = |x|$$?

Accepted Answer

It is a vertical stretch by a factor of 2

Question 7

Which transformation is represented by $$y = f(x + 5)$$?

Accepted Answer

A shift 5 units to the left

Question 8

Given $$f(x) = x^2$, what is the equation for the graph reflected in the x-axis and shifted up by 1 unit?

Accepted Answer

$$y = -x^2$ + 1$$

Question 9

Evaluate the absolute value function $$g(x) = |x| at$$ $$x = -5.25.$$

Accepted Answer

$$5.25$$

Question 10

Which of the following best describes the transformation from $$y = x to$$ $$y = 0.5x$$?

Accepted Answer

Vertical shrink by a factor of 0.5

Question 11

Suppose $$f(x) = \sqrt{x}. $$What is the effect of the transformation $$y = \sqrt{x - 4}$$?

Accepted Answer

Shift the graph 4 units to the right

Question 12

Which of the following is the range of the cube function $$m(x) = x^3$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

A medical device measures the square of the input voltage. If the input is $$-12$$ volts, what is the output according to $$h(x) = x^2$?

Accepted Answer

$$144$$

Question 14

Which of the following transformations will result in a reflection of the graph of $$y = f(x) in $$the x-axis?

Accepted Answer

$$y = -f(x)$$

Question 15

If $$y = |x + 3|$$, how is its graph related to $$y = |x|$$?

Accepted Answer

Shifted 3 units to the left

Question 16

Evaluate the square root function $$n(x) = \sqrt{x} at$$ $$x = 64.$$

Accepted Answer

$$8$$

Question 17

A chemical reaction's rate is modeled by $$f(x) = x^3$. If the concentration is doubled, by what factor does the rate increase?

Accepted Answer

8

Question 18

Which of the following is the correct transformation for $$y = -2|x|$$ from $$y = |x|$$?

Accepted Answer

Vertical stretch by 2 and reflection in the x-axis

Question 19

Given $$f(x) = x^2$, what is the equation for the graph that is reflected in the x-axis and shifted 2 units to the left?

Accepted Answer

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

Elementary Functions and Graph Transformations in College Algebra

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