Q: Which of the following describes the end behavior of $$f(x) = -2x^6$ + 5x^2$ - 1$$?

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

Question 1

Which of the following is the complete factorization of $$x^3$$ - $$3x^2 - 10x$?

Accepted Answer

$$(x - 5)(x + 2)(x)$$

Question 2

Given the function $$f(x) = \log_2$(x+2)$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

$$(-2, \infty)$$

Question 3

If $$f(x) = 2x + 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-7}{2}$$

Question 4

A truck vendor pays weekly fixed costs of $$125$$ and variable costs of $$5.75$$ for each pay-combo sold. If $$x is $$the number of combos sold, which function models the weekly cost $$C(x)$$?

Accepted Answer

$$C(x) = 5.75x + 125$$

Question 5

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 3$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (2x + 3)^2$ - 4$$

Question 6

Which of the following describes the end behavior of $$f(x) = -2x^6$ + 5x^2$ - 1$$?

Accepted Answer

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

Question 7

Given the quadratic equation $$x^2$$ + $$y^2 + 12x - 6y = 0$, what is the center of the circle after completing the square?

Accepted Answer

$$(-6, 3)$$

Question 8

For the function $$f(x) = \frac{8}{x}$$, what are the horizontal and vertical asymptotes?

Accepted Answer

Horizontal: $$y = 0$$, Vertical: $$x = 0$$

Question 9

If $$f(x) = \sqrt{x-2}$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

$$[2, \infty)$$

Question 10

Given $$f(x) = x^3$ - 2x^2$ + 4x - 8$$, which of the following is a possible rational root according to the Rational Root Theorem?

Accepted Answer

$$\pm 1, \pm 2, \pm 4, \pm 8$$

Question 11

A population of bacteria is modeled by $$P(t) = 500e$$^{0.2t}$$, where t$ is in hours. What is the population after 5$ hours?

Accepted Answer

$$P(5) = 500e$$^{1}$$ \approx 1359$$

Question 12

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h} = \frac{(x+h)^2$ - x^2$}{h}$$

Question 13

Given $$f(x) = \frac{2x+1}{x-3}$$, what is the value of $$f^{-1}(4$$)$$?

Accepted Answer

$$x = 5$$

Question 14

Which of the following equations represents a line passing through the points $$(1,3)$$ and $$(2,5)$$?

Accepted Answer

$$y = 2x + 1$$

Question 15

If $$f(x) = x^4$, is the function even, odd, or neither?

Accepted Answer

Even

Question 16

Given the system of equations: $$\begin{cases} 2x + y = 5 \ x - y = 1 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 17

Which of the following is the correct standard form of the complex number $$3 - 7i + 2i$$?

Accepted Answer

$$3 - 5i$$

Question 18

Given the function $$f(x) = \frac{x^2$ - 4}{x - 2}$$, what is the value of $$f(2)$$?

Accepted Answer

$$f(2) is $$undefined

Question 19

A city’s air pollution is modeled by $$P(t) = at^2$ + bt + c. If$$ $$P(0) = 80$$, $$P(2) = 138$$, and $$P(4) = 180$$, which of the following is the correct value for $$c$$?

Accepted Answer

$$c = 80$$

Precalculus Final Exam Review: Comprehensive Study Notes

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