Question 1

Which of the following sets represents the domain of the relation $$\{(1,2), (2,5), (5,7), (7,0)\}$$?

Accepted Answer

$$\{1, 2, 5, 7\}$$

Question 2

Given the relation $$\{(3,1), (-5,0), (10,-2), (7,1)\}$$, what is the range?

Accepted Answer

$$\{1, 0, -2\}$$

Question 3

Which of the following diagrams represents a function?

Accepted Answer

A mapping where each input is connected to exactly one output.

Question 4

Given $$f(x) = x^2$ + 4x + 10$$, what is $$f(-2)$$?

Accepted Answer

$$6$$

Question 5

Which of the following equations does NOT represent a function?

Accepted Answer

$$y = \pm \sqrt{x + 13}$$

Question 6

What is the interval notation for the set $$\{x \mid 2 \leq x \u003c 7\}$$?

Accepted Answer

$$[2, 7)$$

Question 7

Which graph passes the vertical line test and represents a function?

Accepted Answer

A graph where every vertical line intersects the graph at most once.

Question 8

Given the graph of $$f(x) is a $$parabola opening upwards, what is the domain and range?

Accepted Answer

Domain: all real $$x$$, Range: $$y \geq k$$ for some $$k$$

Question 9

If a function $$f(x) is $$even, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x$$

Question 10

What is the slope of the line passing through the points $$(3,4)$$ and $$(6,7)$$?

Accepted Answer

$$1$$

Question 11

Which of the following lines is perpendicular to the line $$y = 2x + 1$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 12

Given $$f(x) = 3x - 2$$ and $$g(x) = 3x - 2 - 2$$, how is the graph of $$g$$ related to $$f$$?

Accepted Answer

The graph of $$g is $$the graph of $$f$$ shifted down.

Question 13

For the piecewise function $$f(x) = \begin{cases} 2x+5 & x \u003c 2 \ x^2$+7 & x \geq 2 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$16$$

Question 14

What is the difference quotient for $$f(x) = 3x + 7$$?

Accepted Answer

$$3$$

Question 15

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(x+1)^2$$

Question 16

Which of the following is the inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+5}{3}$$

Question 17

Given the function $$f(x) = \sqrt{x-7}$$, what is its domain?

Accepted Answer

$$[7, \infty)$$

Question 18

If $$f(x) = x^2$ - 2x + 1$$ and $$g(x) = x - 1$$, what is $$f(g(x))$$?

Accepted Answer

$$(x-1)^2 - 2(x-1) + 1$

Question 19

Which of the following best describes the average rate of change of a function $$f(x)$$ from $$x=a to$$ $$x=b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 20

If two lines are perpendicular and the slope of one is $$m$$, what is the slope of the other?

Accepted Answer

$$-\frac{1}{m}$$

College Algebra: Functions, Graphs, and Linear Equations Study Notes

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