Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 5}$$?

Accepted Answer

$$x \geq 2.5$$

Question 2

A biologist models the population of a bacteria culture with the function $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the approximate population after 4 hours?

Accepted Answer

$$P(4) \approx 500e$$^{1.2}$$ \approx 1660$$

Question 3

Which of the following is the inverse of the function $$f(x) = 3x - 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{3}$$

Question 4

A projectile is launched from the ground with an initial velocity of $$40 m/s. $$Its height $$h in $$meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 40t. At $$what time does the projectile reach its maximum height?

Accepted Answer

$$t = 4.08$$ seconds

Question 5

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 6

Given the function $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 7

A chemical reaction follows the law $$C(t) = 100(1 - e$$^{-0.2t}$$)$$, where $$C(t) is $$the concentration at time $$t in $$minutes. What is the limiting concentration as $$t 	o \infty$$?

Accepted Answer

$$100$$

Question 8

Which of the following is the solution set for the inequality $$2x^2 - 5x + 2$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 2$$

Question 9

If $$f(x) = \log_2$(x-1)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e 1$$

Question 10

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$P(3) = 2$$ thousand dollars at $$x = 3$$ thousand units

Question 11

Which of the following is equivalent to $$\sin(2x)$$ using a double-angle identity?

Accepted Answer

$$2\sin(x)\cos(x)$$

Question 12

A radioactive substance decays according to $$A(t) = 200e$$^{-0.05t}$$, where A$ is the amount in grams and t$ is in years. How much of the substance remains after 10 years?

Accepted Answer

$$A(10) = 200e$$^{-0.5}$$ \approx 121.3$$ grams

Question 13

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 1)$$

Question 14

Which of the following is the sum of the first 10 terms of the arithmetic sequence $$a_n = 3 + 5(n-1)$$?

Accepted Answer

$$S_{10} = 320$$

Question 15

A triangle has sides of length $$7$$, $$24$$, and $$25. $$What is the cosine of the angle opposite the side of length $$25$$?

Accepted Answer

$$\cos C = -1$$

Question 16

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 17

If $$f(x) = 2x^2$ - 3x + 1$$ and $$g(x) = x - 4$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = 2(-2)^2$ - 3(-2) + 1 = 8 + 6 + 1 = 15$$

Question 18

Which of the following is the solution to the equation $$\log_3$(x) + \log_3$(x-2) = 2$$?

Accepted Answer

Question 19

A patient’s temperature $$T (in $$degrees Celsius) is modeled by $$T(t) = 37 + 2\sin\left(\frac{\pi t}{12}\right)$$, where $$t is $$the number of hours after midnight. What is the maximum temperature during the day?

Accepted Answer

$$39$$ degrees Celsius

Precalculus Study Guide: Functions, Graphs, and Equations

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