Q: Given the cost function for electricity $$C(x) = \begin{cases} 20 + 0.1148x & 0 \leq x \leq 700 \\ 20 + 0.1148 \times 700 + 0.1160(x-700) & x \u003e 700 \end{cases}$$, what is the charge for using 1000 kWh in a month?

$$20 + 0.1148 \times 700 + 0.1160 \times 300$$

Q: A real-world scenario: A company charges a flat fee of $$\50$ for up to 100 units of a product, and $$\$$0.75$$ for each additional unit. Which piecewise function models the total cost $$C(x)$$ for $$x$$ units purchased?

$$C(x) = \begin{cases} 50 & 0 \leq x \leq 100 \\ 50 + 0.75(x-100) & x \u003e 100 \end{cases}$$

Question 1

Which of the following best describes the domain and range of the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

Domain: $$[0, \infty)$$, Range: $$[0, \infty)$$

Question 2

Which function from the library is both even and has an absolute minimum at $$x = 0$$?

Accepted Answer

$$f(x) = |x|$$

Question 3

A piecewise-defined function is given by $$f(x) = \begin{cases} 2x + 1 & x \u003c 0 \ -x + 2 & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

Question 4

Which of the following statements is true about the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

It is odd and symmetric with respect to the origin.

Question 5

Given the cost function for electricity $$C(x) = \begin{cases} 20 + 0.1148x & 0 \leq x \leq 700 \ 20 + 0.1148 	imes 700 + 0.1160(x-700) & x \u003e 700 \end{cases}$$, what is the charge for using 1000 kWh in a month?

Accepted Answer

$$20 + 0.1148 	imes 700 + 0.1160 	imes 300$$

Question 6

Which function has a graph that is symmetric with respect to the y-axis and has a range of $$[0, \infty)$$?

Accepted Answer

$$f(x) = |x|$$

Question 7

The greatest integer function $$f(x) = 	ext{int}(x) is $$best described as:

Accepted Answer

The largest integer less than or equal to $$x$$

Question 8

Which of the following is the correct range for the reciprocal function $$f(x) = \frac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 9

A real-world scenario: A company charges a flat fee of $$\50$ for up to 100 units of a product, and $$\$$0.75$$ for each additional unit. Which piecewise function models the total cost $$C(x)$$ for $$x$$ units purchased?

Accepted Answer

$$C(x) = \begin{cases} 50 & 0 \leq x \leq 100 \ 50 + 0.75(x-100) & x \u003e 100 \end{cases}$$

Question 10

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 11

For the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 1 \ 3-x & x \geq 1 \end{cases}$$, what is the range of $$f$$ for $$x in$$ $$[0, 3]$$?

Accepted Answer

$$[1, 4]$$

Question 12

Which function from the library is increasing on its entire domain?

Accepted Answer

$$f(x) = x^3$

Question 13

Suppose $$f(x) = x^2$ and g(x$$) = |x|$$. Which statement is true?

Accepted Answer

Both $$f$$ and $$g$$ are even functions.

Question 14

A function $$f is $$defined as $$f(x) = \begin{cases} 2x+1 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}. $$What is the $$y-$$intercept of $$f$$?

Accepted Answer

$$(0, 1)$$

Question 15

Which of the following best describes the symmetry of the identity function $$f(x) = x$$?

Accepted Answer

Symmetric with respect to the origin

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, which of the following is the domain of g(f(x$$))$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 17

Which of the following is NOT a property of the absolute value function $$f(x) = |x|$$?

Accepted Answer

It is odd.

Question 18

A city charges for water usage as follows: $$\15$ for up to 1000 gallons, and $$\$$0.01$$ per gallon above 1000 gallons. What is the cost for using 1500 gallons?

Accepted Answer

$$15 + 0.01 	imes 500 = \20$

Library of Functions and Piecewise-Defined Functions

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