Question 1

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

Accepted Answer

$$(-2, 5)$$

Question 2

Which of the following functions has a domain of all real numbers except $$x = 0$$?

Accepted Answer

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

Question 3

A function $$f is $$defined by $$f(x) = mx + b. $$Which statement is true about its graph?

Accepted Answer

It is a straight line with slope $$m$$ and $$y-$$intercept $$b.$$

Question 4

Given the function $$f(x) = \sqrt{x-3}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 3$$

Question 5

Which of the following is NOT a function?

Accepted Answer

$$f(x) = \pm \sqrt{x}$$

Question 6

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 7

Which of the following intervals includes both endpoints?

Accepted Answer

$$[a, b]$$

Question 8

If $$f(x) = \frac{1}{x-2}$$, what is the range of $$f$$?

Accepted Answer

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

Question 9

Which of the following best describes the graph of $$y = x^2$?

Accepted Answer

A parabola opening upwards.

Question 10

A scientist models the temperature $$T in $$degrees Celsius as a function of time $$t in $$hours by $$T(t) = 20 + 5t. $$What is the rate of change of temperature per hour?

Accepted Answer

$$5$$ degrees per hour

Question 11

Which of the following is the correct set notation for all $$x$$ such that $$x is a $$rational number?

Accepted Answer

$$\mathbb{Q}$$

Question 12

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of the composite function f(g(x$$))$$?

Accepted Answer

$$x \in \mathbb{R}$$

Question 13

A medical researcher uses the function $$C(t) = 100e$$^{-0.05t}$$ to model the concentration of a drug in the bloodstream over time t$ (in hours). What is the initial concentration?

Accepted Answer

$$100 mg/L$$

Question 14

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 15

Which of the following is the correct interval notation for all $$x$$ such that $$x \geq 2$$?

Accepted Answer

$$[2, \infty)$$

Question 16

A car travels along a straight road, and its position at time $$t is $$given by $$s(t) = 3t + 2. $$What is the velocity of the car?

Accepted Answer

$$3 m/s$$

Question 17

Which of the following is the correct set notation for the set containing only the numbers $$1$$ and $$2$$?

Accepted Answer

$$\{1, 2\}$$

Question 18

Which of the following statements is true about the graph of $$y = x^2$?

Accepted Answer

It passes the vertical line test and is a function.

Question 19

A biologist models the population of bacteria as $$P(t) = 500 \cdot 2^t$$, where $$t is in $$hours. What is the population after $$3$$ hours?

Accepted Answer

$$500 \cdot 2^3$ = 4000$$

Numbers, Functions, and Foundations of Calculus

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