Question 1

Which of the following best describes 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 will shift the graph of $$y = \sin(x) up by 3 $$units?

Accepted Answer

$$y = \sin(x) + 3$$

Question 4

What is the domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 5

Which of the following is the correct inverse of $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-2}{3}$$

Question 6

If $$\log_2$(x) = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 7

A population of bacteria doubles every 3 hours. If the initial population is 200, what is the population after 9 hours?

Accepted Answer

$$1600$$

Question 8

Which of the following is an identity?

Accepted Answer

$$\sin^2$(x) + \cos^2$(x) = 1$$

Question 9

Solve for $$x$$: $$2^x = 16.$$

Accepted Answer

$$x = 4$$

Question 10

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

Accepted Answer

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

Question 11

Given $$\vec{a} = \langle 3, 4 \rangle$$ and $$\vec{b} = \langle 1, 2 \rangle$$, what is $$\vec{a} \cdot \vec{b}$$?

Accepted Answer

$$11$$

Question 12

Which of the following is the sum formula for sine?

Accepted Answer

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

Question 13

If $$\cos(	heta) = \frac{1}{2}$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values of $$	heta$$?

Accepted Answer

$$\frac{\pi}{3}, \frac{5\pi}{3}$$

Question 14

Which of the following is the correct equation for a parabola with vertex at $$(0,0)$$ and focus at $$(0,2)$$?

Accepted Answer

$$x^2 = 8y$

Question 15

What is the sum of the first 10 terms of the arithmetic sequence where $$a_1 = 3$ and d = 2$?

Accepted Answer

$$85$$

Question 16

Which of the following is the correct Law of Cosines?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$\cos C$$

Question 17

If $$f(x) = \log_{10}(x)$$, what is $$f(1000)$$?

Accepted Answer

$$3$$

Question 18

Which of the following is the correct formula for the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 19

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. If N_0$ = 100$$ grams and $$k = 0.2$$, how much remains after 5 hours?

Accepted Answer

$$N(5) = 100e$$^{-1}$$ \approx 36.79$$ grams

Question 20

Which of the following is the correct binomial theorem expansion for $$(x+y)^3$$?

Accepted Answer

$$x^3$$ + $$3x^2y$$ + $$3xy^2$$ + $$y^3$$

Precalculus (MATH 2412) Syllabus and Course Structure – Dallas College

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