Q: Which function below is a piecewise-defined function?

$$f(x) = \begin{cases} x+1, & x \u003c 0 \\ x-1, & x \geq 0 \end{cases}$$

Q: A nurse walks east at 3 mph and another walks north at 4 mph, both starting from the same point. What is the distance between them after 2 hours?

$$d = \sqrt{(3 \times 2)^2$ + (4 \times 2)^2$} = 10$$ miles

Question 1

Which of the following is the correct formula for the distance between two cars, Kiara and Matias, driving away from a hospital at right angles to each other, with speeds of 35 mph and 40 mph, respectively, after $$t$$ hours?

Accepted Answer

$$d(t) = \sqrt{(35t)^2$ + (40t)^2$}$$

Question 2

Given the piecewise function $$f(x) = \begin{cases} x+1, & x  3 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$f(4) = 16$$

Question 3

Which of the following is the graph of the absolute-value function?

Accepted Answer

A V-shaped graph opening upwards

Question 4

For the function $$g(x) = \begin{cases} \frac{1}{3}x + 3, & x \u003c 3 \ -x, & x \geq 3 \end{cases}$$, what is $$g(3)$$?

Accepted Answer

$$g(3) = 0$$

Question 5

Which of the following is NOT a basic function family shown in the study materials?

Accepted Answer

Logarithmic function

Question 6

Evaluate $$f(-3)$$ for $$f(x) = \begin{cases} -\frac{1}{3}x + 2, & x \leq 0 \ x - 5, & x \u003e 0 \end{cases}.$$

Accepted Answer

$$f(-3) = 3$$

Question 7

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

Accepted Answer

$$f(2) = 0$$

Question 8

Which function below is a piecewise-defined function?

Accepted Answer

$$f(x) = \begin{cases} x+1, & x \u003c 0 \ x-1, & x \geq 0 \end{cases}$$

Question 9

Given $$g(x) = \begin{cases} \frac{1}{2}x - 1, & x  1 \end{cases}$$, what is $$g(2)$$?

Accepted Answer

$$g(2) = -4$$

Question 10

For the function $$f(x) = \begin{cases} \frac{x^2$ - 9}{x + 3}, & x 
eq -3 \ 5, & x = -3 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$f(-3) = 5$$

Question 11

Which of the following best describes the reciprocal function $$y = \frac{1}{x}$$?

Accepted Answer

It has two branches, one in the first and one in the third quadrant

Question 12

If $$f(x) = \begin{cases} x^2$ - 4, & x 
eq 2 \ 3, & x = 2 \end{cases}$$, what is the value of $$f(2)$$?

Accepted Answer

$$f(2) = 3$$

Question 13

Which of the following is the correct simplification for $$\frac{x^2$ - 4}{x + 2}$$ for $$x 
eq -2$$?

Accepted Answer

$$x - 2$$

Question 14

A nurse walks east at 3 mph and another walks north at 4 mph, both starting from the same point. What is the distance between them after 2 hours?

Accepted Answer

$$d = \sqrt{(3 	imes 2)^2$ + (4 	imes 2)^2$} = 10$$ miles

Question 15

Which of the following is the correct way to evaluate a piecewise function at a given input?

Accepted Answer

Choose the formula whose domain contains the input value

Types of Functions and Piecewise-Defined Functions in College Algebra

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