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?

$$C(m) = \begin{cases} 20 & 0 \leq m \leq 300 \\ 20 + 0.10(m-300) & m \u003e 300 \end{cases}$$

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

$$C(m) = \begin{cases} 20 & 0 \leq m \leq 300 \ 20 + 0.10(m-300) & m \u003e 300 \end{cases}$$

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 $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, 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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