Question 1

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

Accepted Answer

$$\{ (0,1), (1,2), (2,3), (3,4) \}$$

Question 2

Given the relation $$\{ (2,4), (3,5), (4,6), (5,7) \}$$, what is the domain?

Accepted Answer

$$\{ 2, 3, 4, 5 \}$$

Question 3

A graph passes the vertical line test if:

Accepted Answer

Every vertical line intersects the graph at most once.

Question 4

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

Accepted Answer

$$[0, 9]$$

Question 5

If $$f(x) = 2x - 5$$, what is the value of $$f(3)$$?

Accepted Answer

$$1$$

Question 6

Which of the following statements about function notation is TRUE?

Accepted Answer

$$f(x)$$ and $$y$$ represent the same thing

Question 7

A function $$g is $$defined by $$g(x) = \sqrt{x-1}. $$What is the domain of $$g$$?

Accepted Answer

$$[1, \infty)$$

Question 8

Which of the following graphs does NOT represent a function?

Accepted Answer

A circle centered at the origin

Question 9

If a function $$h$$ has $$x-$$intercepts at $$x = -2$$ and $$x = 3$$, which of the following points must be on the graph of $$h$$?

Accepted Answer

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

Question 10

A function $$f is $$defined by $$f(x) = \frac{1}{x-4}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 11

Suppose a function $$p$$ models the profit (in dollars) from selling $$x$$ units of a product, given by $$p(x) = 50x - 200. $$What is the $$y-$$intercept of this function, and what does it represent?

Accepted Answer

The $$y-$$intercept is $$-200$$, representing the initial loss when no units are sold.

Question 12

Given the function $$f(x) = |x-3|$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 13

A function $$f is $$defined by $$f(x) = 2x^2$ - 8x + 6. $$What is the $$x-$$coordinate of the vertex of the graph of $$f$$?

Accepted Answer

$$x = 2$$

Question 14

If a function $$f$$ has domain $$[0, 5]$$ and range $$[2, 10]$$, which of the following statements is TRUE?

Accepted Answer

The largest $$y-$$value is $$10.$$

Question 15

A real-world scenario: The temperature $$T (in $$degrees Celsius) at time $$t (in $$hours) is modeled by $$T(t) = 10 + 5\sin(\frac{\pi}{12}t). $$What is the range of possible temperatures?

Accepted Answer

$$[5, 15]$$

Question 16

Which of the following is NOT a function?

Accepted Answer

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

Question 17

A function $$f is $$defined by $$f(x) = 3x + 2. If$$ $$f(a) = 11$$, what is the value of $$a$$?

Accepted Answer

$$a = 3$$

Question 18

A function $$f is $$defined on the domain $$[1, 4]$$ and has range $$[2, 8]. $$Which of the following could be the function?

Accepted Answer

$$f(x) = 2x$$

Question 19

If the graph of a function passes through the points $$(0, 5)$$ and $$(2, 0)$$, what are the $$y-$$intercept and $$x-$$intercept, respectively?

Accepted Answer

$$y-$$intercept: $$5$$, $$x-$$intercept: $$2$$

Question 20

A function $$f is $$defined by $$f(x) = \frac{2x+1}{x-3}. $$For which value of $$x is$$ $$f(x)$$ undefined?

Accepted Answer

$$x = 3$$

Functions: Domain, Range, and Function Notation

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