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

$$\tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A)\tan(B)}$$

Question 1

Given the polynomial $$f(x) = x^4$ - 2x^3$ + x^2$, which of the following best describes its end behavior?

Accepted Answer

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

Question 2

Which of the following is the correct number of possible real zeros for the polynomial $$f(x) = x^5$ - 3x^3$ + 2x$$?

Accepted Answer

At most 5 real zeros

Question 3

A rational function $$f(x) = \frac{2x^2$ + 3x - 5}{x^2$ - 4}$$ has which of the following vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 4

Which of the following is the correct application of the Intermediate Value Theorem?

Accepted Answer

If $$f(a)$$ and $$f(b)$$ have opposite signs, then $$f(x)$$ has a zero between $$a$$ and $$b$$

Question 5

Which of the following is the correct equation for the horizontal asymptote of $$f(x) = \frac{3x^2$ + 1}{2x^2$ - 5}$$?

Accepted Answer

$$y = \frac{3}{2}$$

Question 6

If $$f(x) = 2^x$$, which transformation results in the graph of $$g(x) = 2$$^{x-3}$$ + 4$$?

Accepted Answer

Shift right 3 units and up 4 units

Question 7

Which of the following is the correct domain for the function $$f(x) = \log_2$(x-5)$$?

Accepted Answer

$$x \u003e 5$$

Question 8

Which property of logarithms allows you to write $$\log_b(xy) as a $$sum?

Accepted Answer

$$\log_b(xy) = \log_b(x) + \log_b(y)$$

Question 9

Solve for $$x$$: $$2^{x+1} = 16$

Accepted Answer

$$x = 3$$

Question 10

Which of the following is a correct Pythagorean identity?

Accepted Answer

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

Question 11

A right triangle has an angle of $$30^\circ$$ and a hypotenuse of length 10. What is the length of the side opposite the $$30^\circ$$ angle?

Accepted Answer

5

Question 12

Which of the following is the correct double-angle formula for sine?

Accepted Answer

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

Question 13

Solve the trigonometric equation $$\sin(x) = \frac{1}{2}$$ for $$x in$$ $$[0, 2\pi).$$

Accepted Answer

$$x = \frac{\pi}{6}, \frac{5\pi}{6}$$

Question 14

Which of the following is the correct negative angle identity for cosine?

Accepted Answer

$$\cos(-x) = \cos(x)$$

Question 15

If $$f(x) = \frac{1}{x-3}$$, what is the excluded value from the domain?

Accepted Answer

$$x = 3$$

Question 16

Which of the following is the correct formula for the sum of angles for tangent?

Accepted Answer

$$	an(A+B) = \frac{	an(A) + 	an(B)}{1 - 	an(A)	an(B)}$$

Question 17

Which of the following is the correct property to expand $$\log_3$\left(\frac{a}{b}\right)$$?

Accepted Answer

$$\log_3$(a) - \log_3$(b)$$

Question 18

A surveyor measures the angle of elevation to the top of a building as $$60^\circ$$ from a point 20 meters away. What is the height of the building?

Accepted Answer

$$20\sqrt{3}$$ meters

Question 19

Which of the following is the correct sign of $$\sin(	heta) in $$Quadrant II?

Accepted Answer

Positive

Precalculus Exam Review Guide: Polynomial, Rational, Exponential, Logarithmic, and Trigonometric Functions

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