Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$P = \{(-4, 3), (0, 6), (2, 8), (-4, -3)\}$$

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 passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 4

What is the domain of the function $$f(x) = \frac{3}{x+2}$$?

Accepted Answer

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

Question 5

Given $$f(x) = 2x^2$ - 9$$, what is $$f(-1)$$?

Accepted Answer

$$-7$$

Question 6

Which of the following best describes a constant function?

Accepted Answer

$$f(x) is $$the same for every $$x in $$its domain

Question 7

For the function $$y = x^2$ + 3$$, what is the range?

Accepted Answer

$$[3, \infty)$$

Question 8

If a function $$f is $$increasing on an interval $$I$$, which of the following must be true for any $$x_1$$ \u003c $$x_2 in$$ $$I$$?

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$

Question 9

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

Accepted Answer

$$-2$$

Question 10

Which equation represents a vertical line?

Accepted Answer

$$x = 5$$

Question 11

Given the function $$f(x) = ax + b$$ with $$a 
eq 0$$, what is the domain and range?

Accepted Answer

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

Question 12

What is the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$3$$

Question 13

Which of the following is the correct slope formula for a line passing through $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 14

If $$f(x) is $$defined by the set $$\{(-4, 0), (-1, 6), (0, 8), (2, -2)\}$$, what is $$f(0)$$?

Accepted Answer

$$8$$

Question 15

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 16

For the function $$y = |x|$$, what is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[0, \infty)$$

Question 17

Suppose the height of a kite $$h(t) is $$constant for $$5$$ minutes. What does this mean about the graph of $$h(t)$$ during that interval?

Accepted Answer

The graph is a horizontal line segment.

Question 18

Which of the following is NOT a key characteristic of a linear function?

Accepted Answer

Its graph is always a horizontal line.

Question 19

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

Accepted Answer

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

Question 20

A line passes through the point $$(-2, -3)$$ and has slope $$\frac{1}{2}. $$What is its equation in point-slope form?

Accepted Answer

$$y + 3 = \frac{1}{2}(x + 2)$$

Relations, Functions, and Linear Functions: Precalculus Study Notes

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