Q: Which of the following best describes the end behavior of $$p(x) = 3(x+2)^2$(x+4)^3(x-5)(x-7$$)$?

As $$x \to \infty$$, $$p(x) \to \infty$$; as $$x \to -\infty$$, $$p(x) \to -\infty$$

Q: Find the six trigonometric ratios for the triangle with sides $$7$$, $$24$$, and $$25$$, where $$\theta is $$the angle opposite the side of length $$7.$$

$$\sin \theta = \dfrac{7}{25},\ \cos \theta = \dfrac{24}{25},\ \tan \theta = \dfrac{7}{24},\ \csc \theta = \dfrac{25}{7},\ \sec \theta = \dfrac{25}{24},\ \cot \theta = \dfrac{24}{7}$$

Question 1

Which of the following angles is in Quadrant II?

Accepted Answer

$$127.5^\circ$$

Question 2

Convert $$-150^\circ to $$radians.

Accepted Answer

$$-\dfrac{5\pi}{6}$$

Question 3

Given $$\cos(	heta) = -\dfrac{7}{25}$$ and $$	heta is in $$Quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\dfrac{24}{25}$$

Question 4

Find the domain of $$f(x) = \dfrac{1}{x^2$ - 9}.$$

Accepted Answer

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

Question 5

Suppose $$f(x) = \sqrt{x^2$}$$ and $$g(x) = x^2$ - 100x. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$\sqrt{(x^2$ - 100x)^2$}$$

Question 6

How many of the acute angles $$A$$ with $$0^\circ  1$$?

Accepted Answer

SOME

Question 7

Consider the polynomial $$p(x) = 3(x+2)^2$(x+4)^3(x-5)(x-7$$)$$. What is the degree of p(x$$)$?

Accepted Answer

$$7$$

Question 8

For $$f(x) = -2x^2$ - 3x + 4$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$-4x - 2h - 3$$

Question 9

Given $$f(x) = x^2$ - 25x$$ and $$g(x) = \dfrac{1}{x+2}$$, what is the domain of $$(f \cdot g)(x)$$?

Accepted Answer

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

Question 10

Which of the following relations is NOT a function?

Accepted Answer

$$y = \sqrt{x} \pm 2$$

Question 11

Suppose $$g(x) = \sqrt{x-1}$$ and $$f(g(x)) = 3\sqrt{x-1} - \dfrac{1}{\sqrt{x-1}} + 6. $$What is $$f(x)$$?

Accepted Answer

$$3x - \dfrac{1}{x} + 6$$

Question 12

For the function $$f(x) = x^2$ - 2x$$, what is the average rate of change on $$[-1, 2]$$?

Accepted Answer

$$2$$

Question 13

Which of the following best describes the end behavior of $$p(x) = 3(x+2)^2$(x+4)^3(x-5)(x-7$$)$?

Accepted Answer

As $$x 	o \infty$$, $$p(x) 	o \infty$$; as $$x 	o -\infty$$, $$p(x) 	o -\infty$$

Question 14

If $$	heta is in $$Quadrant III and $$\cos(	heta) = -\dfrac{7}{25}$$, what is $$	an(	heta)$$?

Accepted Answer

$$\dfrac{24}{7}$$

Question 15

Find the six trigonometric ratios for the triangle with sides $$7$$, $$24$$, and $$25$$, where $$	heta is $$the angle opposite the side of length $$7.$$

Accepted Answer

$$\sin 	heta = \dfrac{7}{25},\ \cos 	heta = \dfrac{24}{25},\ 	an 	heta = \dfrac{7}{24},\ \csc 	heta = \dfrac{25}{7},\ \sec 	heta = \dfrac{25}{24},\ \cot 	heta = \dfrac{24}{7}$$

Question 16

Which of the following statements is true about continuous functions $$y = f(x)$$ that are increasing on $$[a, b]$$?

Accepted Answer

ALL have a positive average rate of change on $$[a, b]$$

Question 17

Given $$f(x) = x^2$ - 25x$$ and $$g(x) = \dfrac{1}{x+2}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

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

Question 18

If $$\sin(-150^\circ) = -\dfrac{1}{2}$$, what is $$\sec(-150^\circ)$$?

Accepted Answer

$$-2\sqrt{3}$$

Question 19

For the function $$f(x) = \dfrac{1}{x^2$}$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$-\dfrac{2x + h}{x^2$(x+h)^2$$}$

Precalculus Exam 1 Review – Step-by-Step Study Guidance

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