Question 1

Which of the following best describes the domain of the relation $$\{(2, 5), (3, 7), (4, 9)\}$$?

Accepted Answer

$$\{2, 3, 4\}$$

Question 2

Which statement correctly defines a function?

Accepted Answer

A function is a correspondence from the domain to the range such that each element in the domain corresponds to exactly one element in the range.

Question 3

Given the relation $$\{(1, 2), (1, 3), (2, 4)\}$$, is this relation a function?

Accepted Answer

No, because the element $$1 in $$the domain corresponds to two different elements in the range.

Question 4

Which equation does NOT represent $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 5

If $$f(x) = 2x - 5$$, what is $$f(4)$$?

Accepted Answer

$$3$$

Question 6

A medical researcher models the temperature of a patient over time with the function $$T(t) = 98.6 + 0.5t$$, where $$t is $$hours since medication was administered. What is the range of $$T$$ for $$t in$$ $$[0, 4]$$?

Accepted Answer

$$[98.6, 100.6]$$

Question 7

Which of the following graphs fails the vertical line test and therefore does NOT represent a function?

Accepted Answer

A circle centered at the origin, $$x^2$$ + $$y^2 = 9$

Question 8

A chemical reaction is modeled by $$C(t) = 5t^2$ - 2t + 7$$, where $$C is $$concentration and $$t is $$time in hours. What is $$C(3)$$?

Accepted Answer

$$40$$

Question 9

Given the function $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 3$$ and $$x = 1$$

Question 10

For the function $$g(x) = \frac{1}{x-2}$$, what is the domain?

Accepted Answer

$$\{x \mid x 
eq 2\}$$

Question 11

A function $$h(x) is $$graphed and passes through the points $$(-2, 0)$$, $$(0, 3)$$, and $$(2, 0). $$What is the $$y-$$intercept?

Accepted Answer

$$y = 3$$

Question 12

If $$f(x) = x^2$ and g(x$$) = $$x^2 - 3$, how is the graph of g$ related to the graph of f$?

Accepted Answer

The graph of $$g is $$shifted down by 3 units compared to $$f$$

Question 13

Which of the following is NOT a valid range for the function $$f(x) = \sqrt{x}$$ with domain $$[0, 9]$$?

Accepted Answer

$$[0, 9]$$

Question 14

A function $$f is $$graphed and its domain is $$[-2, 5]. $$Which of the following statements is true?

Accepted Answer

The function is defined for all $$x$$ such that $$-2 \leq x \leq 5$$

Question 15

A function $$f(x)$$ models the height of a projectile: $$f(x) = -16x^2$ + 64x + 80$$, where $$x is $$time in seconds. What is the $$y-$$intercept?

Accepted Answer

$$80$$

Question 16

Which of the following statements about intercepts is correct?

Accepted Answer

A function can have more than one x-intercept but at most one y-intercept.

Question 17

If $$f(x) = 3x + 2$$, what is the range of $$f$$ for $$x in$$ $$[-1, 4]$$?

Accepted Answer

$$[-1, 14]$$

Question 18

A function $$f is $$graphed and the graph crosses the x-axis at $$x = -3$$ and $$x = 2. $$What are the x-intercepts?

Accepted Answer

$$(-3, 0)$$ and $$(2, 0)$$

Question 19

Which of the following is the correct function notation for the value of $$f at$$ $$x = 7$$?

Accepted Answer

$$f(7)$$

Chapter 2: Functions and Graphs – Basics of Functions and Their Graphs

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