Question 1

Which of the following sets contains all real numbers $$x$$ such that $$-2 \u003c x \u003c 5$$?

Accepted Answer

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

Question 2

Suppose $$f(x) = \sqrt{x-1}. $$What is the domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Question 3

Which of the following statements about the graph of a function is TRUE?

Accepted Answer

The graph of a function must pass the vertical line test.

Question 4

Given the function $$f(x) = \frac{1}{x}$$, which of the following is the correct domain?

Accepted Answer

$$x 
eq 0$$

Question 5

If $$f(x) = 2x + 3$$, what is the slope of the graph of $$f$$?

Accepted Answer

$$2$$

Question 6

Which of the following is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 7

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

Accepted Answer

$$y \geq 0$$

Question 8

Which of the following intervals represents all real numbers $$x$$ such that $$x is at $$least $$-3$$ and at most $$4$$?

Accepted Answer

$$[-3, 4]$$

Question 9

If $$f(x) = x^2$ - 4$$, what is the value of $$f(-2)$$?

Accepted Answer

$$0$$

Question 10

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

Accepted Answer

$$\mathbb{Q}$$

Question 11

Suppose you are asked to find the distance between the numbers $$a$$ and $$b on $$the real number line. Which formula should you use?

Accepted Answer

$$|a - b|$$

Question 12

Which of the following is the correct definition of the domain of a function $$f$$?

Accepted Answer

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

Question 13

If $$f(x) = \sqrt{x}$$, which of the following is the correct range of $$f$$?

Accepted Answer

$$y \geq 0$$

Question 14

Which of the following is the correct interval notation for the set $$\{x \mid 2 \u003c x \leq 7\}$$?

Accepted Answer

$$(2, 7]$$

Question 15

A function $$f is $$defined by $$f(x) = 3x - 5. $$What is $$f(4)$$?

Accepted Answer

$$7$$

Question 16

Which of the following is a correct example of set-builder notation for the set of all $$x$$ such that $$x is $$greater than $$2$$?

Accepted Answer

$$\{x \mid x \u003e 2\}$$

Question 17

If $$f(x) = x^2$ and g(x) = x + 1$, what is f(g(2$$))$$?

Accepted Answer

$$9$$

Question 18

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

Accepted Answer

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

Question 19

Suppose $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 20

Which of the following is the correct set notation for the intersection of sets $$A$$ and $$B$$?

Accepted Answer

$$A \cap B$$

MATH 221 First Semester Calculus: Numbers and Functions

Study Guide - Practice Questions