$$\{x | -2 \u003c x \\leq 5\}$$

$$f(x) = \begin{cases} x & x \\geq 0 \\ -x & x \u003c 0 \end{cases}$$

Question 1

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

Accepted Answer

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

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 is NOT a property of a function?

Accepted Answer

Each output can have multiple inputs

Question 4

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

Accepted Answer

2

Question 5

Which of the following numbers is a rational number?

Accepted Answer

$$\frac{7}{3}$$

Question 6

If $$f(x) = x^2$, which of the following statements about its graph is true?

Accepted Answer

It passes the vertical line test

Question 7

What is the distance between the numbers $$-3$$ and $$4 on $$the real number line?

Accepted Answer

7

Question 8

Which of the following is the correct set notation for the interval $$(-2, 5]$$?

Accepted Answer

$$\{x | -2 \u003c x \leq 5\}$$

Question 9

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

Accepted Answer

All real numbers except $$x = 0$$

Question 10

Which of the following decimal expansions represents a rational number?

Accepted Answer

$$0.333333...$$

Question 11

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

Accepted Answer

9

Question 12

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

Accepted Answer

The set of all possible outputs $$f(x)$$

Question 13

Which of the following intervals contains all real numbers $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 14

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (g$$ \circ f)(x)$$?

Accepted Answer

All real numbers

Question 15

Which of the following is an example of a piecewise-defined function?

Accepted Answer

$$f(x) = \begin{cases} x & x \geq 0 \ -x & x \u003c 0 \end{cases}$$

Question 16

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

Accepted Answer

It must pass the vertical line test to be a function

Question 17

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

Accepted Answer

36

Question 18

Which of the following is the correct interval notation for all real numbers $$x$$ such that $$-1 \u003c x \u003c 2$$?

Accepted Answer

$$(-1, 2)$$

Question 19

Which of the following is NOT a real number?

Accepted Answer

$$i ($$where $$i^2 = -1$)

Question 20

If $$f(x) = x^2$ and g(x) = x + 2$, what is the range of f(g(x$$))$$ for x$ in $$[0, 2]$$?

Accepted Answer

$$[4, 16]$$

MATH 221: First Semester Calculus – Study Notes (Chapter 1: Numbers and Functions)

Study Guide - Practice Questions