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

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A company’s profit $$P (in $$thousands of dollars) is modeled by the quadratic function $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold (in thousands). 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

Which of the following is the correct composition of the functions $$f(x) = 2x + 1$$ and $$g(x) = x^2$ evaluated at x = 3$ for (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(3) = 2 \cdot 9 + 1 = 19$$

Question 4

Given the function $$f(x) = |x - 4|$$, which statement best describes its graph?

Accepted Answer

It is a V-shaped graph with vertex at $$(4, 0)$$

Question 5

Which of the following is the solution set for the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 6

A population of bacteria grows according to the exponential function $$P(t) = 500 \cdot 2^t$$, where $$t is $$the number of hours. What is the population after 4 hours?

Accepted Answer

$$P(4) = 500 \cdot 2^4$ = 8000$$

Question 7

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

Accepted Answer

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

Question 8

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward: $$h(t) = -4.9t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$h_{max} = 22.41$$ meters

Question 9

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

Accepted Answer

$$(x, y) = (3, 1)$$

Question 10

Which of the following 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 11

Which of the following is the correct graph transformation for $$f(x) = x^2$ to g(x) = (x$$ - $$5)^2 + 3$?

Accepted Answer

Shift right 5 units and up 3 units

Question 12

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

Accepted Answer

$$x = 32$$

Question 13

A medication’s concentration in the bloodstream decreases according to $$C(t) = 100e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 100e$$^{-1}$$ \approx 36.79$$

Question 14

Which of the following is the correct solution to the rational equation $$\dfrac{x}{x-2} = 3$$?

Accepted Answer

$$x = 6$$

Question 15

Which of the following is the correct interval notation for the solution to $$|2x - 5| \leq 7$$?

Accepted Answer

Question 16

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 17

Which of the following is the correct solution to the polynomial equation $$x^3 - 4x = 0$?

Accepted Answer

Question 18

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y + z = 6 \ x - y + z = 2 \ 2x + y - z = 5 \end{cases}$$?

Accepted Answer

$$(x, y, z) = (2, 1, 3)$$

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