Question 1

Which of the following relations is NOT a function?

Accepted Answer

$\{ (1, 2), (2, 3), (1, 4), (4, 5) \}$

Question 2

Given the equation $4x - x^2 = y + 24$, does this equation define $y$ as a function of $x$?

Accepted Answer

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

Question 3

Find the value of the function $f(x) = |x| + 2$ at $x = -5$.

Accepted Answer

$7$

Question 4

Given $f(x) = 9x - 4$ and $g(x) = 2x + 6$, find $(f + g)(1)$.

Accepted Answer

$21$

Question 5

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

Accepted Answer

$3$

Question 6

Find the average rate of change of the function $f(x) = 4x + 11$ from $x = 2$ to $x = 5$.

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 of $f$?

Accepted Answer

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

Question 9

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

Accepted Answer

Even

Question 10

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

Accepted Answer

The function is neither even nor odd, but $f(x) \geq 0$ for all $x$.

Question 11

A company charges a flat fee of \$15 plus \$2 per mile for a delivery. Write the cost $C$ as a function of miles $m$, and find the cost for a 10-mile delivery.

Accepted Answer

$C(m) = 2m + 15$, $C(10) = 35$

Question 12

Given the graph of $f(x) = -x^2 + 8$ (a downward opening parabola), what is the maximum value of $f(x)$ and at what $x$ does it occur?

Accepted Answer

Maximum at $x = 0$, $f(0) = 8$

Question 13

For the function $f(x) = -2x^2 + 8x + 1$, what is the vertex of the parabola?

Accepted Answer

$(2, 9)$

Question 14

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

Accepted Answer

$[-7, \infty)$

Question 15

Given the function $f(x) = x^2 - 6x + 8$, for which value of $x$ does $f(x) = 0$?

Accepted Answer

$x = 2$ and $x = 4$

Question 16

A ball is thrown upward and its height in meters after $t$ seconds is given by $h(t) = -4.9t^2 + 20t + 1$. What is the maximum height reached by the ball?

Accepted Answer

$21$ meters

Question 17

Given the function $f(x) = -x^2 + 8.25$, for which value of $x$ does $f(x) = 0$?

Accepted Answer

$x = \pm 2.872$

Question 18

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

Accepted Answer

$x = 0$

Question 19

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

Accepted Answer

It is symmetric with respect to the $y$-axis.

Question 20

Given the function $f(x) = -x^2 + 8.25$, use the graph to determine the intervals where the function is increasing.

Accepted Answer

$(-\infty, 0)$

College Algebra: Functions, Graphs, and Their Properties

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