Q: A cell phone company charges $20$ per month for $300$ minutes, plus $0.10$ per minute for additional minutes. Which piecewise function models the monthly cost $C$ for $m$ minutes?

$C(m) = \begin{cases} 20 & 0 \leq m \leq 300 \\ 20 + 0.10(m-300) & m > 300 \end{cases}$

Q: Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \\ x^2 & x \geq 0 \end{cases}$, what is the range of $f(x)$?

$(-\infty, 2] \cup [0, \infty)$

Q: Which of the following statements is true about the function $f(x) = x^2$?

The function is even and symmetric with respect to the y-axis.

Q: Which of the following intervals describes where the function $f(x) = x^3$ is decreasing?

The function is never decreasing.

Question 1

Which of the following describes the symmetry of the graph of $f(x) = x^2 - 10$?

Accepted Answer

Symmetric with respect to the y-axis

Question 2

Given the function $f(x) = -x^2 + 4x - 3$, what is the vertex of the parabola?

Accepted Answer

$(2, 1)$

Question 3

For the function $f(x) = x^2 - 4x + 5$, on which interval is the function decreasing?

Accepted Answer

$(-\infty, 2)$

Question 4

Which of the following is the correct difference quotient for $f(x) = x^2$?

Accepted Answer

$\frac{(x+h)^2 - x^2}{h}$

Question 5

A cell phone company charges $20$ per month for $300$ minutes, plus $0.10$ per minute for additional minutes. Which piecewise function models the monthly cost $C$ for $m$ minutes?

Accepted Answer

$C(m) = \begin{cases} 20 & 0 \leq m \leq 300 \ 20 + 0.10(m-300) & m > 300 \end{cases}$

Question 6

Which of the following intervals describes where the function $f(x)$ is increasing, given the graph of a downward opening parabola with vertex at $(2, 1)$?

Accepted Answer

$( 2, \infty )$

Question 7

Given $f(x) = x^2 - 6x + 8$, use the quadratic formula to find the roots.

Accepted Answer

$x = 2$ and $x = 4$

Question 8

Which of the following is the correct formula for the difference quotient of $f(x) = \sqrt{x}$?

Accepted Answer

$\frac{\sqrt{x+h} - \sqrt{x}}{h}$

Question 9

Which of the following equations is symmetric with respect to the origin?

Accepted Answer

$y = x^3$

Question 10

Given the piecewise function $f(x) = \begin{cases} x+2 & x < 0 \ x^2 & x \geq 0 \end{cases}$, what is the range of $f(x)$?

Accepted Answer

$(-\infty, 2] \cup [0, \infty)$

Question 11

Which of the following statements is true about the function $f(x) = x^2$?

Accepted Answer

The function is even and symmetric with respect to the y-axis.

Question 12

For the function $f(x) = -x^2 + 6x - 8$, what is the maximum value?

Accepted Answer

$10$

Question 13

Which of the following intervals describes where the function $f(x) = x^3$ is decreasing?

Accepted Answer

The function is never decreasing.

Question 14

Given the quadratic function $f(x) = ax^2 + bx + c$, which formula gives the x-coordinate of the vertex?

Accepted Answer

$x = -\frac{b}{2a}$

Question 15

Which of the following is the domain of the function $f(x) = \sqrt{x-3}$?

Accepted Answer

$[3, \infty)$

Question 16

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

Accepted Answer

$x^2 + 2x + 1$

Question 17

Which of the following is the correct solution to the equation $x^2 - 5x + 6 = 0$?

Accepted Answer

$x = 2$ and $x = 3$

Question 18

Which of the following is the correct simplified form of the difference quotient for $f(x) = x^2$?

Accepted Answer

$2x + h$

Question 19

Which of the following is the correct interval notation for the range of $f(x) = x^2$?

Accepted Answer

$[0, \infty)$

Study Guide: Functions, Graphs, and Piecewise Functions in College Algebra

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