Question 1

Which of the following relations is NOT a function?

Accepted Answer

$\{ (1, 4), (3, 10), (0, 1), (3, 11), (5, 23) \}$

Question 2

Does the equation $4x - x^2 = y + 24$ define $y$ as a function of $x$?

Accepted Answer

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

Question 3

Given $f(x) = |x| + 2$, what is $f(-5) - f(5)$?

Accepted Answer

$0$

Question 4

Given $f(x) = x^2 + 3x - 1$, what is $f(0)$?

Accepted Answer

$-1$

Question 5

Given $f(x) = x^2 + 3x - 1$ and $g(x) = 2x + 6$, find $(f + g)(1)$.

Accepted Answer

$12$

Question 6

Find the average rate of change of the function $f(x) = 4x + 11$ from $x = 2$ to $x = 6$.

Accepted Answer

$4$

Question 7

Find the slope of the line passing through the points $(-2, 4)$ and $(1, 9)$.

Accepted Answer

$\dfrac{5}{3}$

Question 8

Given the graph of $f(x) = x^2 - 4$ (a parabola opening upwards), what is the domain and range?

Accepted Answer

Domain: $(-\infty, \infty)$, Range: $[-4, \infty)$

Question 9

Given $f(x) = |x|$, determine if the function is even, odd, or neither.

Accepted Answer

Even

Question 10

Suppose a company models its profit with $P(x) = -2x^2 + 8x + 5$, where $x$ is the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $21$ at $x = 2$ thousand units.

Question 11

Given the function $f(x) = |x| - |x - 1|$, what is $f(2)$?

Accepted Answer

$0$

Question 12

Given the function $f(x) = |x|$, which of the following statements is true?

Accepted Answer

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

Question 13

Given the graph of $f(x) = -x^2 + 8$ (as in Figure 2), for which value of $x$ does $f(x) = 8.25$?

Accepted Answer

$x = 0.5$

Question 14

For the function $f(x) = -x^2 + 8$, as shown in Figure 2, on which interval is the function increasing?

Accepted Answer

$(-\infty, 0)$

Question 15

A ball is thrown upward and its height in meters after $t$ seconds is given by $h(t) = -4.9t^2 + 14t + 2$. What is the maximum height reached by the ball?

Accepted Answer

$12$ meters

Question 16

Given $f(x) = |x| - 7$, what is the range of $f$?

Accepted Answer

$[-7, \infty)$

Question 17

Given $f(x) = x^2 - 4x + 3$, for which value(s) of $x$ does $f(x) = 0$?

Accepted Answer

$x = 1$ and $x = 3$

Question 18

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

Accepted Answer

$25$

Question 19

A medical researcher models the spread of a virus with $N(t) = 1000e^{0.2t}$, where $N$ is the number of cases and $t$ is days since the outbreak. How many cases are there after 5 days? (Round to the nearest whole number.)

Accepted Answer

$2718$

Question 20

Given $f(x) = |x|$, which of the following best describes the symmetry of its graph?

Accepted Answer

Symmetric with respect to the $y$-axis

College Algebra: Functions, Graphs, and Their Properties

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