Q: Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \\\\leq 5$$?

$$\\{x \\mid 1 \u003c x \\leq 5\\}$$

Q: Let $$f(x) = \\frac{1}{x-1}. $$What is the domain of $$f$$?

$$(-\\infty, 1) \\cup (1, \\infty)$$

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

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

Question 1

Which of the following sets is the set of all real numbers $$x$$ such that $$1 \u003c x \\leq 5$$?

Accepted Answer

$$\{x \mid 1 \u003c x \leq 5\}$$

Question 2

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

Accepted Answer

$$[2, \infty)$$

Question 3

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

Accepted Answer

Every real number can be represented by a possibly infinite decimal expansion.

Question 4

Suppose $$f(x) = 2x + 3. $$Which of the following best describes the graph of $$f$$?

Accepted Answer

A straight line with slope $$2$$ and $$y-$$intercept $$3$$

Question 5

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

Accepted Answer

$$|a-b|$$

Question 6

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

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 7

A medical thermometer measures temperature in degrees Celsius. If the temperature $$T in $$Fahrenheit is given by $$T = \frac{9}{5}C + 32$$, what is the temperature in Celsius when $$T = 98.6$$?

Accepted Answer

$$37$$

Question 8

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

Accepted Answer

$$f(x) = x^2$

Question 9

Which of the following is NOT a function?

Accepted Answer

The relation $$y^2 = x$

Question 10

A car travels at a constant speed. The distance $$d (in $$kilometers) it travels in $$t$$ hours is given by $$d = 60t. $$What is the range of this function if $$t \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 11

Which of the following intervals represents all $$x$$ such that $$-2 \u003c x \leq 3$$?

Accepted Answer

$$(-2, 3]$$

Question 12

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

Accepted Answer

$$9$$

Question 13

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

Accepted Answer

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

Question 14

Which of the following decimal expansions represents a rational number?

Accepted Answer

$$0.333333\ldots$$

Question 15

Suppose $$f(x) = \sqrt{4-x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$[-2, 2]$$

Question 16

A function $$f is $$defined by $$f(x) = \frac{1}{x^2$-4}. $$For which value of $$x is$$ $$f(x)$$ NOT defined?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 17

Which of the following best describes the range of the function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 18

If $$f(x) = 3x - 5$$, what is the $$x-$$intercept of the graph of $$f$$?

Accepted Answer

$$\frac{5}{3}$$

Question 19

Which of the following is the correct set notation for the interval including all real numbers $$x$$ such that $$x \geq 0$$?

Accepted Answer

$$[0, \infty)$$

Question 20

A pharmaceutical company models the concentration $$C (in mg/L) of a $$drug in the bloodstream $$t$$ hours after injection by $$C(t) = 10e$$^{-0.5t}$$. What is the initial concentration?

Accepted Answer

$$10 mg/L$$

Calculus I Study Notes: Numbers, Functions, and Their Properties

Study Guide - Practice Questions

Study Guide - Flashcards