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 statements best describes the difference between a relation and a function?

Accepted Answer

A relation is any set of ordered pairs, while a function is a relation in which each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is the value of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2h^2 + 4xh - 3h$

Question 3

A company models its revenue with the linear function $$R(x) = 150x + 2000$$, where $$x is $$the number of units sold. What is the revenue if 50 units are sold?

Accepted Answer

$$R(50) = 7500$$

Question 4

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

All real numbers except $$x = 4$$

Question 5

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

Accepted Answer

Question 6

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 7

A biologist models the population of bacteria with the exponential function $$P(t) = 500e$$^{0.2t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 500e$$^{1}$$

Question 8

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

Accepted Answer

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

Question 9

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

Question 10

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

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 11

A chemical reaction is modeled by $$C(t) = 100e$$^{-0.05t}$$, where C$ is the concentration in mg/L and t$ is time in minutes. How long will it take for the concentration to decrease to 50 mg/L?

Accepted Answer

$$t = \frac{\ln(2)}{0.05}$$

Question 12

Which of the following is the correct horizontal asymptote for the rational function $$f(x) = \frac{4x^2$ + 1}{2x^2$ - 5}$$?

Accepted Answer

$$y = \frac{4}{2} = 2$$

Question 13

If $$f(x) = |x - 3|$$, which of the following describes the graph's symmetry?

Accepted Answer

The graph is symmetric about the line $$x = 3$$

Question 14

A medical researcher uses the logarithmic function $$M(x) = \log_{10}(x) to $$model the acidity of a solution. If the acidity is $$x = 1000$$, what is $$M(1000)$$?

Accepted Answer

$$M(1000) = 3$$

Question 15

Which of the following is the solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 16

A business uses the quadratic function $$P(x) = -2x^2$ + 12x - 20 to $$model profit, where $$x is $$the number of products sold. What is the maximum profit, and at how many products sold does it occur?

Accepted Answer

Maximum profit is $$P(3) = 10 at$$ $$x = 3$$

Question 17

Which of the following is the correct solution to the system $$\begin{cases} x^2$ + y^2$ = 25 \ y = 3x \end{cases}$$?

Accepted Answer

$$x = 2, y = 6$$ and $$x = -2, y = -6$$

Question 18

Which of the following is the correct transformation for the function $$f(x) = x^2$ to g(x) = (x$$ - $$4)^2 + 5$?

Accepted Answer

Shift right 4 units and up 5 units

Question 19

Which of the following is the correct solution to the rational inequality $$\frac{x+2}{x-1} \u003e 0$$?

Accepted Answer

$$x \u003e 1 or$$ $$x \u003c -2$$

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