Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(2,5), (3,6), (4,7)\}$$

Question 2

Given the equation $$y = x^2$ + 3$$, which of the following statements is true?

Accepted Answer

It represents a function because each $$x$$ value has exactly one $$y$$ value.

Question 3

What is the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$x 
eq 2$$

Question 4

A medical researcher models the temperature $$T (in$$ °C) of a patient over time $$t (in $$hours) with $$T(t) = 37 + 0.5t. $$What is the range of $$T if$$ $$t is $$between 0 and 4?

Accepted Answer

$$[37, 39]$$

Question 5

Which graph passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 6

Given the function $$f(x) = 2x - 5$$, what is $$f(3)$$?

Accepted Answer

$$6 - 5 = 1$$

Question 7

Which of the following equations does NOT represent $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 8

A chemical reaction is modeled by $$C(t) = 5e$$^{-0.2t}$$, where C$ is the concentration at time t$. What is the domain of C$?

Accepted Answer

$$t \geq 0$$

Question 9

If the graph of a relation fails the vertical line test, what does this indicate?

Accepted Answer

The relation is not a function.

Question 10

Given the function $$f(x) = \sqrt{x-1}$$, what is the domain?

Accepted Answer

$$x \geq 1$$

Question 11

A population of bacteria is modeled by $$P(t) = 1000 \cdot 2^t. $$What is the value of $$P(3)$$?

Accepted Answer

$$8000$$

Question 12

Which of the following is the range of the function $$f(x) = x^2$ for x$ in $$[-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 13

A function $$f is $$defined by $$f(x) = \frac{2x+1}{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$x 
eq 3$$

Question 14

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

Accepted Answer

The range is $$y \geq 0$$

Question 15

A function $$g is $$graphed and passes through the points $$(0,2)$$, $$(1,4)$$, $$(2,8)$$, $$(3,16). $$What is $$g(2)$$?

Accepted Answer

$$8$$

Question 16

Which of the following is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 17

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

Accepted Answer

$$10$$

Question 18

A function $$h is $$defined by $$h(x) = \frac{1}{x}$$ for $$x 
eq 0. $$What is the range of $$h$$?

Accepted Answer

$$y 
eq 0$$

Question 19

Which of the following describes the range of the function $$f(x) = 2x + 1$$ for $$x in$$ $$[0, 5]$$?

Accepted Answer

$$[1, 11]$$

Question 20

A function $$f is $$graphed and you observe that for some $$x$$ values, there are two $$y$$ values. What does this indicate?

Accepted Answer

The graph does not represent a function.

Relations and Functions: Domain, Range, and Graphical Analysis

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