Question 1

Which of the following sets contains only rational numbers?

Accepted Answer

$$\{\frac{3}{4}, -2, 0\}$$

Question 2

Which of the following statements about the real numbers $$\mathbb{R} is $$TRUE?

Accepted Answer

Every rational number is a real number.

Question 3

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 0$$

Question 4

Which of the following functions is NOT linear?

Accepted Answer

$$f(x) = x^2$

Question 5

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

Accepted Answer

$$[0, \infty)$$

Question 6

Which of the following is the correct definition of the distance between two real numbers $$a$$ and $$b$$?

Accepted Answer

$$|a - b|$$

Question 7

Suppose $$A = \{x \mid x \u003e 1\}$$ and $$B = \{x \mid x \u003c 3\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{x \mid 1 \u003c x \u003c 3\}$$

Question 8

Which of the following is a function that passes the vertical line test but fails the horizontal line test?

Accepted Answer

$$f(x) = x^2$

Question 9

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

Accepted Answer

$$x \geq 2$$

Question 10

Which of the following is the correct set notation for the interval containing all real numbers $$x$$ such that $$-2 \u003c x \leq 5$$?

Accepted Answer

$$(-2, 5]$$

Question 11

If $$f(x) = 3x - 7$$, what is the slope of the graph of $$f$$?

Accepted Answer

$$3$$

Question 12

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

Accepted Answer

The set of all possible values $$f(x)$$ can take.

Question 13

Which of the following is NOT a property of real numbers?

Accepted Answer

Existence of multiplicative inverse for zero

Question 14

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

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 15

Which of the following is the correct interval notation for all real numbers except $$0$$?

Accepted Answer

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

Question 16

A function $$f is $$defined by $$f(x) = \frac{1}{x-3}. $$What is the domain of $$f$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 17

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 18

If $$f(x) = x^2$ and g(x) = 2x$, what is f(g(3$$))$$?

Accepted Answer

$$f(g(3)) = f(6) = 36$$

Question 19

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

Accepted Answer

A relation that assigns each element in the domain to exactly one element in the range.

Calculus I Study Notes: Numbers, Functions, and Foundations

Study Guide - Practice Questions