Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$x \geq 2$$

Question 3

Which of the following is NOT a rational number?

Accepted Answer

$$\sqrt{2}$$

Question 4

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

Accepted Answer

$$2$$

Question 5

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

Accepted Answer

$$y = x^2$

Question 6

What is the range of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

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

Question 7

A function $$f is $$defined by $$f(x) = mx + b. If$$ $$f(2) = 7$$ and $$f(5) = 16$$, what is the value of $$m$$?

Accepted Answer

$$3$$

Question 8

Which of the following statements about the real numbers is TRUE?

Accepted Answer

Between any two distinct real numbers, there is always another real number.

Question 9

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

Accepted Answer

$$|a - b|$$

Question 10

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

Accepted Answer

The set of all real numbers $$x$$ for which $$f(x) is $$defined.

Question 11

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

Accepted Answer

$$[0, \infty)$$

Question 12

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

Accepted Answer

$$[2, \infty)$$

Question 13

A student claims that $$0.3333\ldots is a $$rational number. Is this correct?

Accepted Answer

Yes, because $$0.3333\ldots = \frac{1}{3}$$

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

$$\mathbb{Q}$$

Question 15

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

Accepted Answer

$$x \in \mathbb{R}, x 
eq 1$$

Question 16

Which of the following is an example of a function that is not defined for all real numbers?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Question 17

A real-world application: The height $$h (in $$meters) of a ball thrown upward from the ground at time $$t (in $$seconds) is given by $$h(t) = -4.9t^2$ + 20t. $$What is the maximum height reached by the ball?

Accepted Answer

$$20.41$$ meters

Question 18

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$-3 \leq x \u003c 5$$?

Accepted Answer

$$[-3, 5)$$

Question 19

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

Accepted Answer

$$[-4, \infty)$$

Question 20

Suppose $$f(x) is a $$function defined for all $$x$$ except $$x = 0. $$Which of the following could be the formula for $$f(x)$$?

Accepted Answer

$$f(x) = \frac{1}{x}$$

Study Notes: Numbers, Functions, and Foundations of Calculus (MATH 221 First Semester Calculus)

Study Guide - Practice Questions

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