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

Suppose 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 must be sold to achieve it?

Accepted Answer

The maximum profit is $$300$$ thousand dollars when $$x = 10$$ units are sold.

Question 2

Given the function $$f(x) = \sqrt{2x - 8}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 4$$

Question 3

A medication's concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5$ hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4$$

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

$$t = 1.02$$ seconds

Question 6

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 7

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

Accepted Answer

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

Question 8

A population of bacteria triples every $$4$$ hours. If the initial population is $$200$$, what is the population after $$12$$ hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$$C(x) = 0.20x + 30$$

Question 11

Given $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

All real numbers except $$x = 2$$

Question 12

If $$f(x) = 2x + 1$$ and $$f^{-1}(x$$)$$ is its inverse, what is f$$^{-1}$$(7)$$?

Accepted Answer

$$3$$

Question 13

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

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.8$$

Question 14

Which of the following is the solution set for $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6,\ x = -1$$

Question 15

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

Accepted Answer

$$25$$

Question 16

A rectangle has a length that is $$3$$ meters more than twice its width. If the area is $$99 m$^2$$, what is the width?

Accepted Answer

$$6$$ meters

Question 17

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

Accepted Answer

$$x = 5$$

Question 18

If $$f(x) = x^2$ - 2x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, 0)$$

Question 19

A cell phone plan charges $$\40$ per month plus $$\$$0.10$$ per text message. Which function models the total monthly cost $$C$$ for $$x$$ text messages?

Accepted Answer

$$C(x) = 0.10x + 40$$

MATH 162M Precalculus Course Schedule and Topic Overview

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