Question 1

Solve the absolute value equation: $$|3x| = 5. $$What are the solutions for $$x$$?

Accepted Answer

$$x = \frac{5}{3}$$ and $$x = -\frac{5}{3}$$

Question 2

Which of the following is the parent function for $$f(x) = \frac{1}{2}x^2$ - 10$$?

Accepted Answer

$$f(x) = x^2$

Question 3

What transformations are applied to the parent function $$f(x) = x^2$ to obtain f(x$$) = \frac{1}{2}$$(x-10)^2$$?

Accepted Answer

Vertical compression by $$\frac{1}{2}$$ and horizontal shift 10 units right

Question 4

Solve the equation $$|x+2| = 10. $$What are the solutions for $$x$$?

Accepted Answer

$$x = 8$$ and $$x = -12$$

Question 5

Which function from the library of functions has a vertical asymptote at $$x=1$$?

Accepted Answer

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

Question 6

Given $$f(x) = e$$^{x-1}$$, what transformations are applied to the parent function f(x) = e^x$?

Accepted Answer

Horizontal shift 1 unit right

Question 7

Solve the equation $$|2x+5| = 14. $$What are the solutions for $$x$$?

Accepted Answer

$$x = \frac{9}{2}$$ and $$x = -\frac{19}{2}$$

Question 8

Which of the following best describes the transformation from $$f(x) = x^2$ to f(x$$) = $$3(x-1)^2 + 1$?

Accepted Answer

Vertical stretch by 3, shift right 1 unit, shift up 1 unit

Question 9

Solve the equation $$|8x-2| = 7. $$What are the solutions for $$x$$?

Accepted Answer

$$x = \frac{9}{8}$$ and $$x = -\frac{5}{8}$$

Question 10

Which of the following is the correct equation for shifting $$f(x) = x^2$ six units up?

Accepted Answer

$$f(x) = x^2$ + 6$$

Question 11

Student A claims $$f(x) = x^2$ + 6x is$$ $$f(x) = x^2$ shifted 6 units up. Student B claims it is f(x$$) = $$x^2$$ shifted 6 units left. Who is correct?

Accepted Answer

Neither student is correct.

Question 12

Which of the following is the parent function for $$f(x) = 2x - 3$$?

Accepted Answer

$$f(x) = x$$

Question 13

Solve the equation $$|x-5| = 3. $$What are the solutions for $$x$$?

Accepted Answer

$$x = 8$$ and $$x = 2$$

Question 14

Which of the following is the correct equation for shifting $$f(x) = x^2$ six units left?

Accepted Answer

$$f(x) = (x+6)^2$

Question 15

Which of the following best describes the transformation from $$f(x) = x^3$ to f(x$$) = $$x^3 + 6$?

Accepted Answer

Vertical shift 6 units up

Question 16

Which of the following is the parent function for $$f(x) = e$$^{x-1}$$?

Accepted Answer

$$f(x) = e^x$$

Question 17

Which of the following is the parent function for $$f(x) = \frac{2}{x-3}$$?

Accepted Answer

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

Question 18

A real-world application: The cost $$C (in $$dollars) to produce $$x$$ units of a product is modeled by $$C(x) = |2x - 10|. $$For what values of $$x is $$the cost exactly $$30$$?

Accepted Answer

$$x = 20$$ and $$x = -10$$

Question 19

Which of the following best describes the transformation from $$f(x) = x to$$ $$f(x) = 2x - 3$$?

Accepted Answer

Vertical stretch by 2 and vertical shift down 3 units

Precalculus Study Guide: Absolute Value Equations & Library of Functions

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