Q: A cellular phone plan charges $$24.99$$ for up to $$300$$ minutes, and $$0.25$$ per minute for each minute over $$300. $$Which piecewise function models the monthly cost $$C(x)$$ for $$x$$ minutes used?

$$C(x) = \begin{cases} 24.99 & x \leq 300 \\ 0.25(x-300) + 24.99 & x \u003e 300 \end{cases}$$

Question 1

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

Accepted Answer

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

Question 2

A cellular phone plan charges $$24.99$$ for up to $$300$$ minutes, and $$0.25$$ per minute for each minute over $$300. $$Which piecewise function models the monthly cost $$C(x)$$ for $$x$$ minutes used?

Accepted Answer

$$C(x) = \begin{cases} 24.99 & x \leq 300 \ 0.25(x-300) + 24.99 & x \u003e 300 \end{cases}$$

Question 3

Which function is even and has its graph symmetric with respect to the $$y-$$axis?

Accepted Answer

$$f(x) = x^2$

Question 4

For the greatest integer function $$f(x) = 	ext{int}(x)$$, what is $$f(2.7)$$?

Accepted Answer

$$2$$

Question 5

Which of the following statements about the cube function $$f(x) = x^3$ is correct?

Accepted Answer

It is odd and symmetric about the origin.

Question 6

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

Accepted Answer

$$-2$$

Question 7

Which function has no $$x-$$intercept?

Accepted Answer

$$f(x) = b$$ \, (b 
eq 0)$

Question 8

For the function $$f(x) = x - 1$$, what is the $$y-$$intercept?

Accepted Answer

$$-1$$

Question 9

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

Accepted Answer

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

Question 10

A company charges $$C(x) = \begin{cases} 24.99 & x \leq 300 \ 0.25(x-300) + 24.99 & x \u003e 300 \end{cases}$$ for $$x$$ minutes. What is $$C(330)$$?

Accepted Answer

$$32.49$$

Question 11

Which function is increasing for all real numbers?

Accepted Answer

$$f(x) = x^3$

Question 12

For the piecewise function $$f(x) = \begin{cases} -3 & x \leq 0 \ -3 + x^2$ & 0 \u003c x \leq 2 \end{cases}$$, what is the absolute minimum value?

Accepted Answer

$$-3$$

Question 13

Which function is defined as the greatest integer less than or equal to $$x$$?

Accepted Answer

$$f(x) = 	ext{int}(x)$$

Question 14

Which of the following is true about the identity function $$f(x) = x$$?

Accepted Answer

It is symmetric about the origin.

Question 15

For the square function $$f(x) = x^2$, what is the absolute minimum value?

Accepted Answer

$$0$$

Question 16

Which function is neither even nor odd?

Accepted Answer

$$f(x) = b$$ \, (b 
eq 0)$

Question 17

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

Accepted Answer

$$(-\infty, 0)$$

Question 18

Which of the following best describes the range of the constant function $$f(x) = b$$?

Accepted Answer

$$\{b\}$$

Question 19

A piecewise function is defined as $$f(x) = \begin{cases} -3 & x \leq 0 \ -3 + x^2$ & 0  2 \end{cases}. $$What is $$f(4)$$?

Accepted Answer

$$0.5$$

Library of Functions and Piecewise-Defined Functions: Study Notes

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