Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (1,5)\}$$

Question 2

A population of bacteria grows according to $$P(t) = 500 \cdot 2^t. $$What is the average rate of change of the population from $$t=1 to$$ $$t=4$$ hours?

Accepted Answer

$$\frac{P(4)-P(1)}{4-1} = \frac{8000-1000}{3} = 2333.33$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following statements about polynomial functions is TRUE?

Accepted Answer

Polynomials are always continuous for all real numbers.

Question 5

Given $$f(x) = (x-1)^2$(x+2)$$, what is the degree of the polynomial?

Accepted Answer

Degree $$= 3$$

Question 6

A quadratic function $$y = (x+4)^2$ - 5 is $$transformed from its parent function $$y = x^2$. What is the vertex of the transformed function?

Accepted Answer

$$(-4, -5)$$

Question 7

A piecewise function is defined as $$f(x) = \begin{cases} x+2 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}. $$What is the value of $$f(1)$$?

Accepted Answer

$$f(1) = 1$$

Question 8

Solve for $$x$$: $$3^{x+2}$$ = $$3^5$$

Accepted Answer

$$x = 3$$

Question 9

Which of the following is the correct application of the logarithm power rule?

Accepted Answer

$$\log_a(M^p) = p \log_a M$$

Question 10

For the rational function $$f(x) = \frac{x+3}{x-4}$$, what is the vertical asymptote?

Accepted Answer

$$x = 4$$

Question 11

A polynomial $$f(x) = x^3$ - 2x^2$ + x - 2$$ has possible rational zeros according to the Rational Zero Theorem. Which of the following is NOT a possible rational zero?

Accepted Answer

$$3$$

Question 12

Which statement about exponential functions $$y = a \cdot b^x is $$correct?

Accepted Answer

If $$0 \u003c b \u003c 1$$, the function represents exponential decay.

Question 13

A right triangle has legs of length 3 and 4. What is the sine of the angle opposite the leg of length 3?

Accepted Answer

$$\sin	heta = \frac{3}{5}$$

Question 14

Which of the following is a correct trigonometric identity?

Accepted Answer

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

Question 15

Convert the polar coordinates $$(r, 	heta) = (5, \frac{\pi}{3}) to $$rectangular coordinates $$(x, y).$$

Accepted Answer

$$(x, y) = (5 \cos \frac{\pi}{3}, 5 \sin \frac{\pi}{3})$$

Question 16

What is the magnitude of the vector $$\vec{v} = (6, 8)$$?

Accepted Answer

$$|\vec{v}| = \sqrt{6^2$ + 8^2$} = 10$$

Question 17

Given the ellipse $$\frac{(x-2)^2$}{9} + \frac{(y+1)^2$}{4} = 1$$, what is the center of the ellipse?

Accepted Answer

$$(2, -1)$$

Question 18

Solve the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$(x, y) = (3, 2)$$

Question 19

What is the sum of the infinite geometric series $$S = 4 + 2 + 1 + 0.5 + \ldots$$?

Accepted Answer

$$S = \frac{4}{1-0.5} = 8$$

Precalculus Final Exam Study Guide: Key Concepts and Formulas

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