Q: A farmer wants to fence a rectangular plot of land adjacent to a river using 800 ft of fencing, with no fence needed along the river. What dimensions maximize the area?

$$200 \text{ ft} \times 400 \text{ ft}$$

Q: Which of the following describes the end behavior of $$f(x) = -x^4$ + 2x^2$ - 1$$?

$$y \to -\infty as$$ $$x \to \pm\infty$$

Question 1

Given the quadratic function $$f(x) = -2(x-3)^2$ + 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 4)$$

Question 2

A farmer wants to fence a rectangular plot of land adjacent to a river using 800 ft of fencing, with no fence needed along the river. What dimensions maximize the area?

Accepted Answer

$$200 	ext{ ft} 	imes 400 	ext{ ft}$$

Question 3

What is the maximum area that can be enclosed by the farmer's fence in the previous problem?

Accepted Answer

$$80,000 	ext{ ft}^2$$

Question 4

Which of the following is NOT a polynomial?

Accepted Answer

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

Question 5

Given $$f(x) = x^3$ - 2x^2$ + x - 2$$, which of the following is a zero of the function?

Accepted Answer

$$x = 2$$

Question 6

For the rational function $$f(x) = \frac{x^2$ - 9}{x - 3}$$, what is the equation of the vertical asymptote?

Accepted Answer

$$x = 3$$

Question 7

Which of the following describes the end behavior of $$f(x) = -x^4$ + 2x^2$ - 1$$?

Accepted Answer

$$y 	o -\infty as$$ $$x 	o \pm\infty$$

Question 8

If a polynomial has a zero at $$x = 2$$ with multiplicity 3, what happens to the graph at $$x = 2$$?

Accepted Answer

The graph crosses the x-axis at $$x = 2$$

Question 9

Solve the system of equations: $$\begin{cases} x + 2y = 4 \ 2x - y = 1 \end{cases}$$

Accepted Answer

$$(x, y) = (1, 1.5)$$

Question 10

Which of the following is the correct equation for the axis of symmetry for $$f(x) = 2x^2$ - 4x + 1$$?

Accepted Answer

$$x = 1$$

Question 11

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

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 12

Which of the following is the correct solution set for the inequality $$2x - 5 \u003e 3$$?

Accepted Answer

$$x \u003e 4$$

Question 13

If $$f(x) = x^2$ - 4x + 3$$, what are the x-intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 14

Which of the following best describes the horizontal asymptote of $$f(x) = \frac{3x^2$ + 1}{x^2$ - 2}$$?

Accepted Answer

$$y = 3$$

Question 15

For the function $$f(x) = (x-2)^2$(x+1)$$, what is the degree of the polynomial?

Accepted Answer

$$3$$

Question 16

Which of the following is the correct vertex form for the quadratic $$f(x) = x^2$ - 6x + 5$$?

Accepted Answer

$$f(x) = (x-3)^2$ - 4$$

College Algebra: Polynomial and Rational Functions, Optimization, and Systems of Equations

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