$$Q = \{x \mid x \text{ is a rational number}\}$$

$$x \in \mathbb{R}, x \neq 2, x \neq -2$$

Question 1

Which of the following sets represents all real numbers $$x$$ such that $$1 \u003c x \u003c 6$$?

Accepted Answer

$$B = \{x \mid 1 \u003c x \u003c 6\}$$

Question 2

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$x \geq 2$$

Question 3

Which of the following is the correct definition of a function?

Accepted Answer

A rule which tells you how to compute the value $$f(x)$$ for each $$x in $$the domain.

Question 4

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 2$$

Question 5

A straight line passes through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$). $$What is the formula for its slope?

Accepted Answer

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

Question 6

Which of the following functions passes the vertical line test but fails the horizontal line test?

Accepted Answer

$$y = x^2$

Question 7

If $$f(x) = mx + b is a $$linear function, what does the constant $$b$$ represent?

Accepted Answer

The $$y-$$intercept of the line

Question 8

Suppose you are modeling the distance between two points on the real number line, $$a$$ and $$b. $$What is the correct formula for the distance?

Accepted Answer

$$|a - b|$$

Question 9

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 10

A function $$f is $$defined by $$f(x) = x^2$. What is the range of f$?

Accepted Answer

$$[0, \infty)$$

Question 11

Which of the following sets contains only rational numbers?

Accepted Answer

$$\{\frac{1}{2}, \frac{3}{4}, 5\}$$

Question 12

If the decimal expansion of a number repeats, what type of number is it?

Accepted Answer

A rational number

Question 13

Which of the following intervals includes both endpoints?

Accepted Answer

$$[a, b]$$

Question 14

Which of the following is the correct set notation for the set of all $$x$$ such that $$x is a $$rational number?

Accepted Answer

$$Q = \{x \mid x 	ext{ is a rational number}\}$$

Question 15

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x^2$ - 4}$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 2, x 
eq -2$$

Question 16

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

Accepted Answer

$$x \geq 0$$

Question 17

Which of the following is a correct example of set-builder notation for the interval $$[2, 5)$$?

Accepted Answer

$$\{x \mid 2 \leq x \u003c 5\}$$

Question 18

Which of the following statements about the real number line is TRUE?

Accepted Answer

The distance between two numbers $$a$$ and $$b is$$ $$|a-b|$$

Question 19

Suppose you are given the function $$f(x) = \frac{1}{x}. $$Which value of $$x is $$NOT in the domain?

Accepted Answer

$$x = 0$$

Question 20

Which of the following is the correct formula for a linear function?

Accepted Answer

$$f(x) = mx + b$$

Numbers, Functions, and Graphs – Foundations of Calculus

Study Guide - Practice Questions