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

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

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

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

Question 1

Which of the following sets contains 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 $$x in a $$given domain.

Question 4

Suppose $$f(x) = 2x + 3. $$What is the slope of the graph of $$f$$?

Accepted Answer

$$2$$

Question 5

Given the function $$f(x) = \frac{1}{x-2}$$, which value is NOT in the domain?

Accepted Answer

$$x = 2$$

Question 6

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

Accepted Answer

A graph passes the vertical line test if every vertical line intersects it at most once.

Question 7

If $$f(x) = x^2$, what is the range of f$?

Accepted Answer

$$[0, \infty)$$

Question 8

A real-world example: The distance between two points $$a$$ and $$b on $$the number line is given by which formula?

Accepted Answer

$$|a - b|$$

Question 9

Which of the following is a linear function?

Accepted Answer

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

Question 10

Suppose you are modeling the height $$h of a $$ball thrown upward as a function of time $$t by$$ $$h(t) = -4.9t^2$ + 20t + 2. $$What is the physical meaning of the domain of this function?

Accepted Answer

The set of all $$t \geq 0$$ for which the ball is above the ground.

Question 11

Which of the following intervals includes all real numbers $$x$$ such that $$2 \leq x \u003c 5$$?

Accepted Answer

$$[2, 5)$$

Question 12

If $$f(x) = \sqrt{x}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 0$$

Question 13

Which of the following is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 14

What is the 200th digit after the period in the decimal expansion of $$\frac{1}{7}$$?

Accepted Answer

$$2$$

Question 15

Which of the following sets is the solution to $$x^2 = 2$?

Accepted Answer

$$\{-\sqrt{2}, \sqrt{2}\}$$

Question 16

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

Accepted Answer

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

Question 17

If $$f(x) = \frac{1}{x}$$, what is the range of $$f$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 18

Which of the following is the correct formula for the distance between two points $$x_1$$ and $$x_2 on $$the real number line?

Accepted Answer

$$|x_1$ - x_2$|$$

Question 19

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

Accepted Answer

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

Numbers, Functions, and Graphs: Foundations of Calculus

Study Guide - Practice Questions

Study Guide - Flashcards