Question 1

Which of the following best describes the definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 19$$

Question 3

Which transformation occurs when the graph of $$y = f(x) is $$changed to $$y = f(x-4) + 2$$?

Accepted Answer

Shift right 4 units and up 2 units.

Question 4

A company models its profit $$P as a $$function of time $$t (in $$years) by $$P(t) = 5000e$$^{0.08t}$$. What is the profit after 5 years?

Accepted Answer

$$P(5) = 5000e$$^{0.4}$$ \approx 7459$$

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

A circle has center at $$(2, -3)$$ and radius $$5. $$Which equation represents this circle?

Accepted Answer

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

Question 8

Which of the following is a solution to the equation $$2x^2 - 5x + 3 = 0$?

Accepted Answer

$$x = 1$$

Question 9

A population of bacteria grows according to $$N(t) = 1000e$$^{0.05t}$$, where t$ is in hours. How long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.05} \approx 13.86$$ hours

Question 10

Which of the following is the correct application of the Law of Sines for triangle $$ABC$$ with sides $$a$$, $$b$$, $$c$$ opposite angles $$A$$, $$B$$, $$C$$?

Accepted Answer

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

Question 11

Which formula is used to find the midpoint between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 12

Which of the following is the correct expression for the sum of angles formula for sine?

Accepted Answer

$$\sin(A+B) = \sin A \cos B + \cos A \sin B$$

Question 13

If $$\log_{10} x = 3$$, what is the value of $$x$$?

Accepted Answer

$$x = 1000$$

Question 14

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 15

A vector has components $$\vec{v} = \langle 3, 4 \rangle. $$What is its magnitude?

Accepted Answer

$$|\vec{v}| = \sqrt{3^2$ + 4^2$} = 5$$

Question 16

Which of the following is the correct formula for the dot product of vectors $$\vec{a} = \langle a_1$, a_2$ \rangle$$ and $$\vec{b} = \langle b_1$, b_2$ \rangle$$?

Accepted Answer

$$\vec{a} \cdot \vec{b} = a_1$ b_1$ + a_2$ b_2$

Question 17

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 18

Which of the following is the correct expression for the distance between points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Precalculus (Math 109) Syllabus and Course Structure – Study Guide

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