Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

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 solution set of the equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2$$ and $$x = 3$$

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 how many units should be sold to achieve it?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$5$$

Question 5

A population of bacteria triples every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

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

Question 6

Solve for $$x$$: $$\log_2$(x) + \log_2$(x-2) = 3.$$

Accepted Answer

$$x = 4$$

Question 7

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

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

Question 8

A ball is thrown upward from a height of 2 meters with an initial velocity of 20 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 2. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$ seconds

Question 9

Which of the following is the inverse function of $$f(x) = \frac{2x - 5}{3}$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{3x + 5}{2}$$

Question 10

Given the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 11

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 12

A radioactive substance decays according to $$A(t) = 100e$$^{-0.2t}$$, where A$ is the amount remaining after t$ years. How much remains after 5 years (rounded to the nearest whole number)?

Accepted Answer

$$37$$

Question 13

Which of the following is the solution to the inequality $$|2x - 3| \u003c 5$$?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 14

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

Accepted Answer

$$(2, 3)$$

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

$$C = 0.20x + 30$$

Question 16

Which of the following is the solution to $$\sqrt{x + 5} = x - 1$$?

Accepted Answer

$$x = 2$$

Question 17

A quadratic function models the height $$h (in $$meters) of a diver above water as $$h(t) = -5t^2$ + 10t + 3. $$How long is the diver above 8 meters?

Accepted Answer

$$0 \u003c t \u003c 2$$

Question 18

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

Accepted Answer

$$x = 3$$

Question 19

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

Accepted Answer

$$[1, \infty)$$

Math 245 Tentative Schedule: College Algebra Chapter Overview

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