Q: Given $f(x) = \frac{1}{x-2}$, what is the domain of $f$ in interval notation?

$(-\infty, 2) \cup (2, \infty)$

Q: If $f(x) = x^2 - 4x - 7$, what is the $x$-intercept(s) of the function?

$(2 + \sqrt{11}, 0)$ and $(2 - \sqrt{11}, 0)$

Question 1

Evaluate the function $F(x) = x^2 - 4x - 7$ at $x = -3$.

Accepted Answer

$14$

Question 2

Given the function $F(x) = x^2 - 4x - 7$, what is $F(x+h)$?

Accepted Answer

$x^2 + 2xh + h^2 - 4x - 4h - 7$

Question 3

Which of the following best describes the domain of the function $f(x) = \sqrt{x-1}$?

Accepted Answer

$[1, \infty)$

Question 4

A function $f(x)$ is said to be even if:

Accepted Answer

$f(-x) = f(x)$

Question 5

Given the piecewise function $f(x) = \begin{cases} x+6 & x < -2 \ x-6 & x \geq -2 \end{cases}$, what is the range of $f(x)$?

Accepted Answer

$(-\infty, \infty)$

Question 6

Find the average rate of change of the function $f(x) = x^2 - 3x$ from $x = -2$ to $x = 5$.

Accepted Answer

$4$

Question 7

Which of the following functions is odd?

Accepted Answer

$f(x) = x^3 - x$

Question 8

Given $f(x) = x^2 - 4x - 7$, what is the simplified form of the difference quotient $\frac{f(x+h) - f(x)}{h}$?

Accepted Answer

$2x + h - 4$

Question 9

Which of the following intervals describes where the function $f(x)$ is increasing, given the graph of a downward-opening parabola with vertex at $(2, 0)$?

Accepted Answer

$(-\infty, 2)$

Question 10

A real-world application: The height $h$ (in meters) of a ball thrown upward from a building is given by $h(t) = -5t^2 + 20t + 50$. What is the average rate of change of height from $t = 1$ to $t = 3$ seconds?

Accepted Answer

$-15$ m/s

Question 11

Given $f(x) = x^2 - 4x - 7$ and $g(x) = x - 1$, find $(f \circ g)(2)$.

Accepted Answer

$-10$

Question 12

Which of the following is the equation of a line in slope-intercept form that passes through $(2,4)$ and has a slope of $-3$?

Accepted Answer

$y = -3x + 10$

Question 13

Find the inverse of the function $f(x) = x^2 - 5$ for $x \geq 0$.

Accepted Answer

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

Question 14

Given $f(x) = \frac{1}{x-2}$, what is the domain of $f$ in interval notation?

Accepted Answer

$(-\infty, 2) \cup (2, \infty)$

Question 15

If $f(x) = 2x + 1$ and $g(x) = x^2 - 3$, what is $(f + g)(x)$?

Accepted Answer

$x^2 + 2x - 2$

Question 16

Which of the following best describes the $y$-intercept of the line $3x - 4y = 8$?

Accepted Answer

$(0, -2)$

Question 17

Given $f(x) = x^2 - 4x - 7$, what is the value of $x$ for which $f(x) = 3$?

Accepted Answer

$x = 5$ or $x = -1$

Question 18

Which of the following is the equation of a line in slope-intercept form that is perpendicular to $4x - 2y = 8$ and passes through $(0, 5)$?

Accepted Answer

$y = \frac{1}{2}x + 5$

Question 19

If $f(x) = x^2 - 4x - 7$, what is the $x$-intercept(s) of the function?

Accepted Answer

$(2 + \sqrt{11}, 0)$ and $(2 - \sqrt{11}, 0)$

Functions and Graphs: College Algebra Chapter 1 Review

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