Question 1

Which of the following best describes the domain of a function $$f(x)$$?

Accepted Answer

The set of all possible $$x-$$values for which $$f(x) is $$defined.

Question 2

Given the points $$A(2, 3)$$ and $$B(5, 7)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(5-2)^2$ + (7-3)^2$}$$

Question 3

Which of the following is the correct midpoint formula for points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 4

If a function $$f(x)$$ has a denominator, which values must be excluded from the domain?

Accepted Answer

Values that make the denominator zero.

Question 5

What is the slope of the line passing through the points $$(1, 2)$$ and $$(4, 8)$$?

Accepted Answer

$$\frac{8-2}{4-1}$$

Question 6

Which of the following is the general point-slope form of a line?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 7

If a line has a slope of $$m = 0$$, what can you say about the line?

Accepted Answer

It is a horizontal line.

Question 8

Which of the following is the correct way to write the equation of a line in slope-intercept form?

Accepted Answer

$$y = mx + b$$

Question 9

If a function passes the vertical line test, what does this mean?

Accepted Answer

Each $$x-$$value has only one $$y-$$value.

Question 10

Given $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 11

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible $$y-$$values for which $$f(x) is $$defined.

Question 12

If you are given the equation $$y = 3x + 2$$, what is the $$y-$$intercept?

Accepted Answer

$$2$$

Question 13

Which of the following is true about the slopes of parallel lines?

Accepted Answer

They are equal.

Question 14

If a line has the equation $$x = 5$$, what type of line is this?

Accepted Answer

A vertical line.

Question 15

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$d = \sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 16

A real-world application: A chemist needs to mix two solutions. The concentration of solution A is $$x$$ and solution B is $$y. If $$the total concentration must be $$10$$, which equation represents this scenario?

Accepted Answer

$$x + y = 10$$

Question 17

If the graph of a function opens upwards and passes through the origin, which of the following could be its equation?

Accepted Answer

$$y = x^2$

Question 18

If a function $$f(x) is $$defined as $$f(x) = \frac{1}{x}$$, which value must be excluded from the domain?

Accepted Answer

$$x = 0$$

Question 19

Which of the following is the correct way to find the $$x-$$intercept of a function $$f(x)$$?

Accepted Answer

Set $$f(x) = 0$$ and solve for $$x.$$

College Algebra Quiz 2 Review – Functions, Graphs, and Linear Equations

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