Question 1

Given the relation $$\{(-1, -1), (7, 4), (3, 0), (-5, -1)\}$$, what is the domain in set notation?

Accepted Answer

$$\{-1, 7, 3, -5\}$$

Question 2

Which of the following relations is NOT a function?

Accepted Answer

$$\{(2, 3), (2, 5), (4, 7)\}$$

Question 3

Given the equation $$x^2$$ + $$y^2 = 25$, is this equation a function of x$?

Accepted Answer

No, because for some $$x$$ values there are two corresponding $$y$$ values.

Question 4

Which of the following best describes the range of the relation $$\{(-1, -1), (7, 4), (3, 0), (-5, -1)\} in $$set notation?

Accepted Answer

$$\{-1, 0, 4\}$$

Question 5

Suppose $$f(x) = x^2$ - 6x + 23. $$What is $$f(-5)$$?

Accepted Answer

$$78$$

Question 6

Given the function $$h(x) = 7 - x^2$, evaluate h(9$$)$$.

Accepted Answer

$$-74$$

Question 7

Which of the following equations is written explicitly in terms of $$x$$?

Accepted Answer

$$y = 2x + 3$$

Question 8

A relation is given by the set $$\{(a, b), (c, d), (e, f), (a, g)\}. Is $$this relation a function?

Accepted Answer

No, because the input $$a is $$paired with two different outputs.

Question 9

Given $$p(x) = 22 + 4x - 13$$, what is $$p(4)$$?

Accepted Answer

$$25$$

Question 10

Which of the following best describes the vertical line test for functions?

Accepted Answer

A relation is a function if no vertical line intersects its graph at more than one point.

Question 11

Given $$g(x) = x^3$ + 3x^2$ + 7x - 4$$, what is $$g(-2)$$?

Accepted Answer

$$-30$$

Question 12

Suppose $$q(x) = \sqrt{6 - 2x}. $$For which value of $$x is$$ $$q(x)$$ defined?

Accepted Answer

$$x = -15$$

Question 13

Given $$f(x) = x^3$ + x^2$, what is f(3y^2$)$$?

Accepted Answer

$$(3y^2)^3$ + (3y^2$)^2$$

Question 14

Which of the following real-world scenarios can be modeled by a function?

Accepted Answer

Assigning each student at a university a unique student ID number.

Question 15

Given $$h(x) = x^2$ - x - 1$$, what is $$h(2a + 7)$$?

Accepted Answer

$$(2a + 7)^2$ - (2a + 7) - 1$$

Question 16

If $$k(x) = 4x + 7$$, what is $$k(m - 1)$$?

Accepted Answer

$$4(m - 1) + 7$$

Question 17

Given the equation $$x - 4y = 20$$, solve for $$y$$ explicitly in terms of $$x.$$

Accepted Answer

$$y = \dfrac{x - 20}{-4}$$

Question 18

Suppose $$f(x) = x^2$ - 6x + 23$$ models the cost (in dollars) to produce $$x$$ units of a product. What is the cost to produce 0 units?

Accepted Answer

$$23$$

Question 19

Given $$a(x) = 2x - 7 + 1$$, what is $$a(17)$$?

Accepted Answer

$$28$$

Precalculus Study Guide: Relations, Domain & Range, Functions, and Function Notation

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