Q: If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

$$f(g(2)) = 3 \times 4 - 7 = 5$$

Question 1

Which of the following is the correct solution to the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the function $$P(x) = -5x^2$ + 40x - 60$$, where $$x is $$the number of units sold (in hundreds). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$\140$$,000$$ at x = 4$ (400 units)

Question 3

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 4

If $$f(x) = 3x - 7$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 3 	imes 4 - 7 = 5$$

Question 5

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h (in $$feet) after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$After how many seconds does the ball hit the ground again?

Accepted Answer

$$t = 2$$ seconds

Question 6

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 7

Solve for $$x$$: $$\log_2$(x) = 5.$$

Accepted Answer

$$x = 32$$

Question 8

A biologist models the population of a bacteria culture by $$P(t) = 500e$$^{0.3t}$$, where t$ is in hours. What is the population after 5$ hours, rounded to the nearest whole number?

Accepted Answer

$$P(5) \approx 2241$$

Question 9

Which of the following equations represents a line parallel to $$y = -2x + 5$$ and passing through the point $$(1, 3)$$?

Accepted Answer

Question 10

Which of the following is the solution set for the inequality $$2x - 5 \u003c 9$$?

Accepted Answer

$$x \u003c 7$$

Question 11

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 12

A medication’s concentration in the bloodstream is modeled by $$C(t) = 20e$$^{-0.5t}$$, where t$ is in hours. What is the concentration after 3$ hours, rounded to two decimal places?

Accepted Answer

$$C(3) \approx 4.46$$

Question 13

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

Accepted Answer

Question 14

Which of the following is the correct simplification of $$\dfrac{2x^2$ - 8}{4x}$$ for $$x 
eq 0$$?

Accepted Answer

$$\dfrac{x - 2}{2}$$

Question 15

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for driving $$x$$ miles?

Accepted Answer

$$C = 0.2x + 30$$

Question 16

Which of the following is the solution to $$|3x - 5| = 7$$?

Accepted Answer

$$x = 4 or$$ $$x = -\dfrac{2}{3}$$

Question 17

If $$f(x) = \dfrac{1}{x}$$ and $$g(x) = x + 2$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$\dfrac{1}{x + 2}$$

Question 18

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

Accepted Answer

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

Question 19

A radioactive substance decays according to $$A(t) = 100e$$^{-0.2t}$$, where t$ is in years. How much of the substance remains after 10$ years, rounded to the nearest whole number?

Accepted Answer

$$A(10) \approx 37$$

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