Q: Which of the following tables represents a linear function?

Table 1: $$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ y & 27 & 25 & 23 & 21 \end{array}$$

Q: Given the right triangle below, which expression represents $$\sin \theta$$?

$$\frac{\text{opposite}}{\text{hypotenuse}}$$

Question 1

Given the function $$y = \sqrt{\frac{x-2}{x-3}}$$, what is the domain of the function?

Accepted Answer

$$(-\infty, 2] \cup (3, \infty)$$

Question 2

Which of the following tables represents a linear function?

Accepted Answer

Table 1: $$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \ y & 27 & 25 & 23 & 21 \end{array}$$

Question 3

A population grows by 3% per minute. If the initial amount is 15 mg, which formula models the amount $$A$$ after $$t$$ minutes?

Accepted Answer

$$A = 15(1.03)^t$$

Question 4

A student club sells 500 shirts at $$\10$ each. For every $$\$$1$$ increase in price, they sell 10 fewer shirts. What is the demand function $$N(P)$$?

Accepted Answer

$$N(P) = 500 - 10(P - 10)$$

Question 5

Which of the following is the correct formula for continuously compounded interest?

Accepted Answer

$$A(t) = Pe$$^{rt}$$

Question 6

Given the right triangle below, which expression represents $$\sin 	heta$$?

Accepted Answer

$$\frac{	ext{opposite}}{	ext{hypotenuse}}$$

Question 7

What is $$\sin \left(\frac{\pi}{3}\right)$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 8

Which of the following best describes the graph of $$y = \sin t$$?

Accepted Answer

It is symmetric with respect to the origin and has a period of $$2\pi.$$

Question 9

If $$f(x) = x^2$ + kx + 9$$, for which value(s) of $$k$$ does $$f(x)$$ have exactly one real root?

Accepted Answer

$$k = 6 or$$ $$k = -6$$

Question 10

A car is purchased for $$\20$$,000$$ and loses half its value every year. When will the car be worth $$\$$3,000$$?

Accepted Answer

$$t = \frac{\ln(0.15)}{\ln(0.5)} \approx 2.74$$ years

Question 11

Which of the following is the range of the inverse sine function $$\sin$$^{-1}$$(x)$$?

Accepted Answer

$$[-\frac{\pi}{2}, \frac{\pi}{2}]$$

Question 12

Suppose a population is 100 and grows to 150 in 3 months, following exponential growth. When will the population reach 300?

Accepted Answer

$$6$$ months

Question 13

Which of the following statements is true about exponential functions?

Accepted Answer

The ratio of consecutive outputs is constant for evenly spaced inputs.

Question 14

Given the compound interest formula $$A(t) = P \left(1 + \frac{r}{n}\$$right)^{nt}$$, what is the value of A(5$$)$$ if P = 1000$, r = 0.05$, n = 12$, and t = 5$?

Accepted Answer

$$A(5) \approx 1283$$

Question 15

Which of the following is the correct value for $$\cos\left(\frac{5\pi}{3}\right)$$?

Accepted Answer

$$\frac{1}{2}$$

Precalculus and Calculus Foundations: Functions, Trigonometry, and Exponential Models

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