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

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 $$f(x) = \sqrt{2x - 6}$$?

Accepted Answer

$$x \geq 3$$

Question 2

A company models its weekly profit with the function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in hundreds). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$26 at$$ $$x = 2$$ hundred units

Question 3

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

Accepted Answer

$$(f \circ g)(x) = (2x + 1)^2$ - 4$$

Question 4

Which transformation maps the graph of $$y = x^2$ to y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units, up 2 units

Question 5

A ball is thrown upward from a height of 5 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 5. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 1.02$$ seconds

Question 6

Solve the inequality $$2x - 3 \u003e 5.$$

Accepted Answer

$$x \u003e 4$$

Question 7

If $$f(x) = \log_2$(x - 1)$$, what is the domain of $$f$$?

Accepted Answer

$$x \u003e 1$$

Question 8

Given $$f(x) = 3x - 2$$, find the inverse function $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 9

Which of the following describes the range of the function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 10

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where t$ is in years. What is the amount remaining after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.79$$

Question 11

Solve for $$x$$: $$\log_3$(x + 5) = \log_3$(x^2 - 1$$)$.

Accepted Answer

$$x = 2$$

Question 12

Which of the following is the correct composition $$(g \circ f)(x) if$$ $$f(x) = x + 2$$ and $$g(x) = x^2$?

Accepted Answer

$$(g \circ f)(x) = (x + 2)^2$

Question 13

A population grows according to $$P(t) = 500 \cdot 2$$^{0.3t}$$. What is the population after 5 years?

Accepted Answer

$$P(5) = 500 \cdot 2$$^{1.5}$$ \approx 1414$$

Question 14

Which of the following is the solution to the equation $$2^{x+1} = 32$?

Accepted Answer

$$x = 4$$

Question 15

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

Accepted Answer

$$(-\infty, \infty)$$

Question 16

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

Accepted Answer

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

Question 17

Solve for $$x$$: $$3^{2x} = 81$.

Accepted Answer

$$x = 2$$

Question 18

Which of the following is the correct inverse of $$f(x) = \frac{2x - 1}{3}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3x + 1}{2}$$

Question 19

A medication is eliminated from the body according to $$C(t) = 50e$$^{-0.2t}$$, where C$ is the concentration in mg/L and t$ is time in hours. What is the concentration after 8 hours?

Accepted Answer

$$C(8) = 50e$$^{-1.6}$$ \approx 10.1 mg/L$$

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