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

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

Question 1

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

Accepted Answer

Question 2

A quadratic function models the height $$h (in $$meters) of a ball $$t$$ seconds after it is thrown: $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height the ball reaches?

Accepted Answer

$$21.96$$ meters

Question 3

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

Accepted Answer

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

Question 4

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 12x - 16$$, where $$x is $$the number of units sold (in thousands). For what value of $$x is $$the profit maximized?

Accepted Answer

$$x = 4$$

Question 5

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

Accepted Answer

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

Question 6

Which of the following is the solution set for the inequality $$2x^2 - 5x + 2$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 2$$

Question 7

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(2x + 1)^2$ - 4$$

Question 8

Which of the following is the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 9

A population of bacteria triples every 4 hours. If the initial population is 200, what is the population after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 10

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 11

Which of the following is the solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 12

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$x 
eq 2$$

Question 13

Which of the following describes the range of the function $$f(x) = |x - 3|$$?

Accepted Answer

$$y \geq 0$$

Question 14

A rational function has a vertical asymptote at $$x = 2$$ and a horizontal asymptote at $$y = 0. $$Which of the following could be its equation?

Accepted Answer

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

Question 15

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 1)$$

Question 16

Which of the following is the correct solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

Question 17

Which of the following is the correct graph transformation for $$f(x) = (x+2)^2$ - 5$$ compared to $$f(x) = x^2$?

Accepted Answer

Shift left 2 units and down 5 units

Question 18

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

Accepted Answer

$$15$$

Question 19

Which of the following is the solution to the equation $$|3x - 4| = 5$$?

Accepted Answer

$$x = 3$$, $$x = -\frac{1}{3}$$

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