Question 1

Given the quadratic function $$f(x) = 4(x - 6)^2$ + 4$$, what are the coordinates of its vertex?

Accepted Answer

$$(6, 4)$$

Question 2

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

Accepted Answer

Rises to the left and rises to the right

Question 3

A farmer has 228 feet of fencing to enclose a rectangular region. What are the dimensions of the rectangle that maximize the enclosed area?

Accepted Answer

$$57 ft by$$ $$57 ft$$

Question 4

Find the x-intercepts of $$f(x) = x^4$ - 121x^2$ and state the behavior at each intercept.

Accepted Answer

$$0 ($$touches and turns), $$11 ($$crosses), $$-11 ($$crosses)

Question 5

Determine the symmetry of the graph of $$f(x) = x(2 - x^2$).$$

Accepted Answer

Origin symmetry

Question 6

What is the horizontal asymptote of $$f(x) = \frac{6x}{2x^2$ + 1}$$?

Accepted Answer

$$y = 0$$

Question 7

Find the zeros and their multiplicities for $$f(x) = 4(x - 3)(x + 6)^4$. State whether the graph crosses or touches the x-axis at each zero.

Accepted Answer

$$3 ($$multiplicity 1, crosses), $$-6 ($$multiplicity 4, touches and turns)

Question 8

Solve the system: $$x + y + z = -3$$, $$x - y + 5z = 3$$, $$4x + y + z = 6. $$What is the solution?

Accepted Answer

$$(3, -5, -1)$$

Question 9

Which of the following rational functions has a slant (oblique) asymptote $$y = x + 11$$?

Accepted Answer

$$f(x) = \frac{x^2$ + 7x - 9}{x - 4}$$

Question 10

Find the vertical asymptotes of $$h(x) = \frac{x + 1}{x^2$ - 1}.$$

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 11

Given $$f(x) = x^3$ + 4x^2$ - 3x - 2$$, what is the end behavior of the function?

Accepted Answer

Falls to the left and rises to the right

Question 12

Solve the system by substitution: $$-9x - y = 20$$, $$y = x^2$ - 6. $$What is one solution?

Accepted Answer

$$(-7, 43)$$

Question 13

Which of the following polynomial functions has y-axis symmetry?

Accepted Answer

$$f(x) = x^4$ - 9x^2$

Question 14

Find the zeros of $$f(x) = x^3$ + x^2$ - 30x.$$

Accepted Answer

$$x = 0, x = -6, x = 5$$

Question 15

Which of the following systems of equations has the solution $$(-8, -9)$$?

Accepted Answer

$$xy = 72, x + y = -17$$

Question 16

For the polynomial $$f(x) = (x + 1)(x - 8)(x - 1)^2$, which zero does the graph touch and turn around at?

Accepted Answer

$$x = 1$$

Question 17

Which of the following rational functions has a horizontal asymptote at $$y = 5$$?

Accepted Answer

$$g(x) = \frac{25x^2$}{5x^2$ + 1}$$

Question 18

A system of inequalities is graphed, and the solution set is the region above the line $$x - y = 0$$ and below the line $$x + 2y = 2. $$Which point is in the solution set?

Accepted Answer

$$(0, 1)$$

College Algebra Test 3 Review – Step-by-Step Guidance

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