$$(-\\infty, -2) \\cup (-2, 2) \\cup (2, \\infty)$$

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

$$f(x) = \\begin{cases} x^2$ & x \\geq 0 \\ \\ -x & x \u003c 0 \\end{cases}$$

$$\\mathbb{R} \\setminus \\{0\\}$$

Question 1

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

Accepted Answer

$$(-2, 5]$$

Question 2

Suppose $$f(x) = 3x - 7. $$What is the slope of the graph of $$f$$?

Accepted Answer

$$3$$

Question 3

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 4

Given the function $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 5

A function $$f is $$defined by $$f(x) = \frac{1}{x^2$ - 4}. $$Which of the following describes its domain?

Accepted Answer

$$(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$$

Question 6

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

Accepted Answer

The graph of a function passes the vertical line test.

Question 7

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

Accepted Answer

$$[0, \infty)$$

Question 8

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt{-1}$$

Question 9

A car travels along a straight road. Its position at time $$t is $$given by $$s(t) = 4t + 2. $$What is the velocity of the car?

Accepted Answer

$$4$$

Question 10

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

Accepted Answer

$$[0, \infty)$$

Question 11

Suppose $$f(x) = 2x + 5$$ and $$g(x) = x^2$. What is (f$$ \circ g)(x)$$?

Accepted Answer

$$2x^2 + 5$

Question 12

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 13

If $$f(x) = x^2$ - 4x + 3$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 14

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

Accepted Answer

$$|a - b|$$

Question 15

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

Accepted Answer

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

Question 16

Which of the following is a correct example of a piecewise defined function?

Accepted Answer

$$f(x) = \begin{cases} x^2$ & x \geq 0 \ \ -x & x \u003c 0 \end{cases}$$

Question 17

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

Accepted Answer

$$(-\infty, 3)$$

Question 18

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

Accepted Answer

$$9$$

Question 19

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

Accepted Answer

$$\mathbb{R} \setminus \{0\}$$

Numbers, Functions, and Graphs – Foundations of Calculus

Study Guide - Practice Questions