Question 1

Given the piecewise function $$f(x) = \begin{cases} -3x+2 & x \u003c -2 \ x^2$ & x \geq -2 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-3(-3)+2 = 11$$

Question 2

Given $$g(x) = \begin{cases} x+4 & x \u003c 2 \ x^2$-2 & x \geq 2 \end{cases}$$, what is $$g(2)$$?

Accepted Answer

$$2^2-2 = 2$

Question 3

For the piecewise function $$h(x) = \begin{cases} 2x-1 & x \u003c 0 \ 3 & x \geq 0 \end{cases}$$, what is the domain?

Accepted Answer

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

Question 4

Given $$f(x) = \begin{cases} x^2$-4 & x \u003c 1 \ 2x+1 & x \geq 1 \end{cases}$$, what is the range?

Accepted Answer

$$(-\infty, -3) \cup [3, \infty)$$

Question 5

Which of the following best describes the graph of $$g(x) = \begin{cases} 2x+1 & x \u003c 2 \ x^2$ & x \geq 2 \end{cases}$$?

Accepted Answer

A line for $$x \u003c 2$$ and a parabola for $$x \geq 2$$

Question 6

Evaluate $$f(0)$$ for $$f(x) = \begin{cases} -x+2 & x \u003c 1 \ x^2$-1 & x \geq 1 \end{cases}.$$

Accepted Answer

$$-0+2 = 2$$

Question 7

A hospital uses a piecewise function to model the cost $$C(x) of a $$treatment, where $$x is $$the number of days: $$C(x) = \begin{cases} 200x & x \leq 3 \ 150x+150 & x \u003e 3 \end{cases}. $$What is the cost for 5 days?

Accepted Answer

$$150 	imes 5 + 150 = 900$$

Question 8

Which value of $$x$$ causes a change in the formula used for $$f(x) = \begin{cases} 3x-2 & x \u003c 4 \ x^2$ & x \geq 4 \end{cases}$$?

Accepted Answer

$$x = 4$$

Question 9

Given $$f(x) = \begin{cases} x+1 & x \u003c 0 \ 2x-3 & x \geq 0 \end{cases}$$, which of the following is true?

Accepted Answer

$$f(-1) = 0$$ and $$f(1) = -1$$

Question 10

A company charges for shipping as follows: $$S(w) = \begin{cases} 5w & w \leq 10 \ 50 + 3(w-10) & w \u003e 10 \end{cases}$$, where $$w is $$the weight in kg. What is the cost to ship a 12 kg package?

Accepted Answer

$$50 + 3 	imes (12-10) = 56$$

Question 11

For $$f(x) = \begin{cases} x^2$ & x \u003c 2 \ 4x-3 & x \geq 2 \end{cases}$$, which interval describes the domain?

Accepted Answer

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

Question 12

If $$f(x) = \begin{cases} 2x+1 & x \u003c 1 \ x^2$-1 & x \geq 1 \end{cases}$$, what is $$f(1)$$?

Accepted Answer

$$1^2 - 1 = 0$

Question 13

Which of the following is the correct range for $$g(x) = \begin{cases} -x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$?

Accepted Answer

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

Question 14

A medication is administered according to $$M(t) = \begin{cases} 10t & t \u003c 5 \ 50 & t \geq 5 \end{cases}$$, where $$t is $$time in hours. How much medication is given at $$t = 6$$?

Accepted Answer

$$50$$

Question 15

Given $$f(x) = \begin{cases} 2x-1 & x \u003c 3 \ x^2$ & x \geq 3 \end{cases}$$, what is $$f(4)$$?

Accepted Answer

$$4^2 = 16$

Study Guide: Piecewise Functions in Calculus

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