Q: Which of the following is a piecewise-defined function?

$$f(x) = \begin{cases} 2x+5, & x\u003c0 \\ x^2$-1, & x \geq 0 \end{cases}$$

Question 1

Which of the following best describes a function in mathematical terms?

Accepted Answer

A rule that assigns each element in a set A to exactly one element in a set B.

Question 2

Given the function $$f(x) = \sqrt{x-4}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 4$$

Question 3

A biologist is studying the number of bacteria in a culture over time. Which is the independent variable and which is the dependent variable?

Accepted Answer

Time is the independent variable; number of bacteria is the dependent variable.

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (1,4)\}$$

Question 5

If $$f(x) = 3x^2$ + 5x - 12$$, what is the net change in $$f as$$ $$x$$ changes from $$1 to$$ $$3$$?

Accepted Answer

$$f(3) - f(1) = 24$$

Question 6

Which of the following is a piecewise-defined function?

Accepted Answer

$$f(x) = \begin{cases} 2x+5, & x\u003c0 \ x^2$-1, & x \geq 0 \end{cases}$$

Question 7

A graph passes the vertical line test if:

Accepted Answer

No vertical line intersects the graph at more than one point.

Question 8

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = 3x^2$ - 5$$

Question 9

Suppose the cost $$C of $$mailing a package depends on its weight $$w$$ according to a table. Which of the following best describes this relationship?

Accepted Answer

Cost is a function of weight.

Question 10

Given $$f(x) = 2x^2$ - 3x + 4$$, find $$f(a+h) - f(a) in $$terms of $$a$$ and $$h.$$

Accepted Answer

$$4ah + 2h^2$ - 3h$$

Question 11

Which of the following is NOT a valid way to represent a function?

Accepted Answer

By a random list of unrelated numbers.

Question 12

If $$f(x) = x^2$ and g(x) = x+1$, what is f(g(2$$))$$?

Accepted Answer

$$9$$

Question 13

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible output values.

Question 14

A function is continuous if:

Accepted Answer

Its graph can be drawn without lifting your pencil.

Question 15

Which of the following is the correct function notation for 'the output of $$f at$$ $$x$$'?

Accepted Answer

$$f(x)$$

Question 16

If $$f(x) = x^2$ + 2x$$, what is $$f(-3)$$?

Accepted Answer

$$3$$

Question 17

Which of the following real-world scenarios is best modeled by a piecewise-defined function?

Accepted Answer

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile.

Question 18

Which of the following is a root function?

Accepted Answer

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

Question 19

If $$f(x) = 2x + 5$$, and $$f(a) = 11$$, what is the value of $$a$$?

Accepted Answer

$$3$$

Question 20

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Introduction to Functions in Precalculus

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