Question 1

Which of the following relations is NOT a function?

Accepted Answer

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

Question 2

Given the relation $$R = \{(-4, -2), (-1, 0), (1, 2), (3, 5)\}$$, what is the domain and range?

Accepted Answer

Domain: $$\{-4, -1, 1, 3\}$$; Range: $$\{-2, 0, 2, 5\}$$

Question 3

Which graph below does NOT represent a function?

Accepted Answer

A graph of a circle centered at the origin.

Question 4

What is the range of the function $$f(x) = 2x - 5$$?

Accepted Answer

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

Question 5

Given $$f(x) = x^2$ + 3$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[3, \infty)$$

Question 6

If $$f(x) = \frac{3}{x+2}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 7

Which of the following statements about the vertical line test is TRUE?

Accepted Answer

If every vertical line intersects the graph at no more than one point, the relation is a function.

Question 8

Given $$f(x) = 2x^2$ - 9$$, find $$f(-1).$$

Accepted Answer

$$-7$$

Question 9

Suppose the height $$h of a $$kite (in feet) as a function of time $$t (in $$minutes) is graphed and is constant from $$t=10 to$$ $$t=15. $$What does this mean about the kite's motion during this interval?

Accepted Answer

The kite is hovering at the same height.

Question 10

Which of the following describes a function that is decreasing on an interval $$I$$?

Accepted Answer

For $$x_1  f$$($$x_2$$)$$

Question 11

What is the slope of the line passing through the points $$(-2, 4)$$ and $$(2, -6)$$?

Accepted Answer

$$-2.0$$

Question 12

Which of the following is the equation of a vertical line passing through $$x = 5$$?

Accepted Answer

$$x = 5$$

Question 13

What is the average rate of change of $$f(x)$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 14

Which of the following is the standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 15

If $$f(x) is a $$constant function, which of the following is true for all $$x in $$the domain?

Accepted Answer

$$f(x)$$ remains the same for all $$x$$

Question 16

Given the equation $$2x - 5y = 10$$, what is the slope of the line?

Accepted Answer

$$\frac{2}{5}$$

Question 17

Which of the following is the correct function notation for 'y is a function of x'?

Accepted Answer

$$f(x)$$

Question 18

If $$f(x) = 3x + 2$$, what is $$f(-1)$$?

Accepted Answer

$$-5$$

Question 19

Which of the following best describes the domain of a function defined by an algebraic expression?

Accepted Answer

All real numbers except those that lead to division by zero or even roots of negative numbers.

Question 20

A line with a positive slope rises from ______ to ______.

Accepted Answer

left to right

Relations, Functions, and Linear Functions: Precalculus Study Notes

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