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

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

Question 1

Which of the following sets represents the domain of the function $$f(x) = \sqrt{5 - 2x}$$?

Accepted Answer

$$(-\infty, 2.5]$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units must be sold to achieve it?

Accepted Answer

Maximum profit is $$26$$ thousand dollars at $$x = 2$$ thousand units.

Question 3

Which of the following describes the transformation of the parent function $$f(x) = x^2$ to g(x$$) = $$-2(x-3)^2 + 5$?

Accepted Answer

Reflect over the $$x-$$axis, vertically stretch by $$2$$, shift right $$3$$ units, and up $$5$$ units.

Question 4

Given the function $$f(x) = \dfrac{3x+1}{x-2}$$, which of the following statements is true?

Accepted Answer

The function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 3.$$

Question 5

If $$f(x) = 2x - 1$$ and $$g(x) = x^2$ + 3$$, what is $$(f \circ g)(2)$$?

Accepted Answer

$$9$$

Question 6

Which of the following equations represents a direct variation?

Accepted Answer

$$y = 5x$$

Question 7

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 8

Which of the following is the inverse of the function $$f(x) = 3x - 4$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+4}{3}$$

Question 9

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 10

Solve for $$x$$: $$|2x - 5| = 9$$

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 11

Which of the following is the solution set for the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$(1, 3)$$

Question 12

Given $$f(x) = x^2$ - 6x + 8$$, what are the zeros of the function?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 13

Which of the following is a power function?

Accepted Answer

$$f(x) = 7x$$^{3/2}$$

Question 14

If $$f(x) = \log_2$(x-1)$$, what is the domain of $$f$$?

Accepted Answer

$$(1, \infty)$$

Question 15

Which of the following is equivalent to $$\log_5$(25x)$$?

Accepted Answer

$$2 + \log_5$(x)$$

Question 16

A medication’s concentration in the bloodstream decreases by $$12\%$$ per hour. If the initial concentration is $$C_0$$, which function models the concentration $$C$$ after $$t$$ hours?

Accepted Answer

$$C(t) = C_0$ \cdot (0.88)^t$$

Question 17

Which of the following is NOT a function?

Accepted Answer

A relation where $$x = 2$$ maps to both $$y = 3$$ and $$y = 5$$

Question 18

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

Accepted Answer

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

Question 19

Solve for $$x$$: $$2^{x+1} = 32$

Accepted Answer

$$x = 4$$

Question 20

A car’s value depreciates according to the function $$V(t) = 20000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value of the car after $$3$$ years?

Accepted Answer

$$12206.25$$

MAC1105 College Algebra: Structured Study Guide Based on Course Schedule

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