Q: Which of the following is the correct set notation for the union of sets $$A = \{x \mid x \u003e 1\}$$ and $$B = \{x \mid x \u003c -1\}$$?

$$\{x \mid x \u003e 1 \text{ or } x \u003c -1\}$$

Question 1

Which of the following sets is NOT a subset of the real numbers $$\mathbb{R}$$?

Accepted Answer

The set of all complex numbers $$\mathbb{C}$$

Question 2

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

Accepted Answer

$$x \geq 2$$

Question 3

Which of the following statements about the decimal expansion of rational numbers is TRUE?

Accepted Answer

All rational numbers have either terminating or repeating decimal expansions.

Question 4

A function $$f is $$defined by $$f(x) = \frac{1}{x-3}. $$Which of the following is TRUE about its graph?

Accepted Answer

It is defined for all real numbers except $$x = 3$$

Question 5

Which of the following best describes the range of the function $$f(x) = x^2$ for x$$ \in \mathbb{R}$$?

Accepted Answer

All non-negative real numbers

Question 6

A pharmaceutical company models the concentration $$C(t) of a $$drug in the bloodstream by $$C(t) = 5e$$^{-0.2t}$$, where t$ is in hours. What is the initial concentration?

Accepted Answer

$$5$$

Question 7

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

Accepted Answer

$$(-2, 5]$$

Question 8

A function $$f is $$defined as $$f(x) = 2x + 1. $$Which of the following statements is TRUE?

Accepted Answer

The graph of $$f is a $$straight line with slope 2.

Question 9

Which of the following is the correct set notation for the set of all real numbers $$x$$ such that $$x^2$$ \u003c 9$$?

Accepted Answer

$$\{x \mid -3 \u003c x \u003c 3\}$$

Question 10

A real-world scenario: The temperature $$T in a $$chemical reaction is modeled by $$T(t) = 20 + 10\sin(\pi t/12)$$, where $$t is in $$hours. What is the maximum temperature reached?

Accepted Answer

$$30$$

Question 11

Which of the following is NOT a function?

Accepted Answer

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

Question 12

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

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 13

Which of the following best describes the vertical line test?

Accepted Answer

A test to determine if a graph represents a function by checking that no vertical line intersects the graph more than once.

Question 14

Suppose $$f(x) = \frac{1}{x}$$ and $$g(x) = x^2$. What is the domain of the composite function f(g(x$$))$$?

Accepted Answer

Question 15

Which of the following is the correct interval notation for the set $$\{x \mid x \geq 0\}$$?

Accepted Answer

$$[0, \infty)$$

Question 16

A medical test measures the glucose level $$G(t) in a $$patient’s blood, modeled by $$G(t) = 100 - 5t$$ for $$0 \leq t \leq 10. $$What is the glucose level after 6 hours?

Accepted Answer

$$80$$

Question 17

Which of the following is the correct set notation for the union of sets $$A = \{x \mid x \u003e 1\}$$ and $$B = \{x \mid x \u003c -1\}$$?

Accepted Answer

$$\{x \mid x \u003e 1 	ext{ or } x \u003c -1\}$$

Question 18

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

Accepted Answer

$$|a - b|$$

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