Q: Which of the following describes the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 1$$?

$$f(x) \to -\infty as$$ $$x \to \infty$$ and $$x \to -\infty$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$

Question 3

Given the function $$f(x) = 3x - 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 4

A bacteria culture triples every 4 hours. If the initial population is 500, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 3$$^{t/4}$$

Question 5

Which of the following is the solution set for $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 6

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

Accepted Answer

$$(f \circ g)(3) = 25$$

Question 7

A ball is thrown upward from a height of 2 meters with an initial velocity of 12 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 12t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 1.22$$ seconds

Question 8

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 9

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

Accepted Answer

$$x = 4$$

Question 10

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

Accepted Answer

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

Question 11

A car's value depreciates by 15% each year. If the car is worth $20,000 now, what will its value be in 3 years?

Accepted Answer

$$20,000 	imes (0.85)^3$

Question 12

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

Accepted Answer

$$x = 2,\ y = 1$$

Question 13

Which of the following describes the end behavior of $$f(x) = -2x^4$ + 5x^2$ - 1$$?

Accepted Answer

$$f(x) 	o -\infty as$$ $$x 	o \infty$$ and $$x 	o -\infty$$

Question 14

If $$\log_3$(x) = 4$$, what is the value of $$x$$?

Accepted Answer

$$x = 81$$

Question 15

A right triangle has legs of length $$x$$ and $$x+1$$, and hypotenuse $$5. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 16

Which of the following is the equation of the line passing through $$(1,2)$$ and perpendicular to $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$y = 2x$$

Question 17

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

Accepted Answer

$$x 
eq 2$$

Question 18

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.2t}$$, where t$ is in years. If the initial amount is 100$ grams, how much remains after 5$ years?

Accepted Answer

$$100 e$$^{-1}$$ grams

Question 19

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 5 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = 5$$

Question 20

A parabola has vertex at $$(2, -3)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

$$y = a(x - 2)^2$ - 3$$,\ a \u003e 0$

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