Question 1

What is the slope of the line passing through the points $$(6, -3)$$ and $$(6, -4)$$?

Accepted Answer

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Question 2

Find the equation of the line in slope-intercept form that passes through $$(-5, -7)$$ and $$(-7, -2).$$

Accepted Answer

$$y = -\frac{5}{2}x - \frac{39}{2}$$

Question 3

Given the equation $$x + 2y - 1 = 0$$, what are the slope and $$y-$$intercept?

Accepted Answer

Slope: $$-\frac{1}{2}$$, $$y-$$intercept: $$\frac{1}{2}$$

Question 4

Write the equation of the line passing through $$(2, -3)$$ and parallel to $$y = -2x + 3 in $$point-slope form.

Accepted Answer

$$y + 3 = -2(x - 2)$$

Question 5

Find the average rate of change of $$f(x) = 2x$$ from $$x_1 = 2$ to x_2$ = 8.$$

Accepted Answer

$$\frac{1}{3}$$

Question 6

What is the distance between the points $$(-2, -2)$$ and $$(1, 7)$$?

Accepted Answer

$$3\sqrt{10}$$

Question 7

Find the midpoint of the segment with endpoints $$(-4, -1)$$ and $$(2, 4).$$

Accepted Answer

$$(-1, \frac{3}{2})$$

Question 8

Write the standard form of the equation of the circle with center $$(9, -10)$$ and radius $$\sqrt{14}.$$

Accepted Answer

$$(x - 9)^2$ + (y + 10)^2$ = 14$$

Question 9

Find the vertex of the parabola defined by $$f(x) = 2x^2$ - 4x - 8.$$

Accepted Answer

$$(1, -10)$$

Question 10

A person throws a ball from the top of a $$304-$$foot building. The height is modeled by $$s(t) = -16t^2$ + 64t + 304. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$2$$ seconds

Question 11

What is the domain of $$f(x) = \frac{6x}{x + 6}$$?

Accepted Answer

$$(-\infty, -6) \cup (-6, \infty)$$

Question 12

How can the graph of $$f(x) = \frac{1}{x-4} + 10 be $$obtained from $$y = \frac{1}{x}$$?

Accepted Answer

Shift right $$4$$ units and up $$10$$ units

Question 13

For the rational function $$g(x) = \frac{x}{x(x+5)}$$, what are the vertical asymptotes and holes?

Accepted Answer

Vertical asymptote: $$x = -5$$, Hole: $$x = 0$$

Question 14

Which rational function has a horizontal asymptote $$y = 2$$?

Accepted Answer

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

Question 15

Find the slant asymptote of $$f(x) = \frac{x^2$ + 7x - 9}{x - 4}.$$

Accepted Answer

$$y = x + 11$$

Question 16

A manufacturer finds that revenue is $$R(p) = -5p^2$ + 1190p. $$What is the maximum revenue?

Accepted Answer

$$70,805$$

Question 17

You have $$236$$ feet of fencing to enclose a rectangular region. What is the maximum area you can enclose?

Accepted Answer

$$3481$$ square feet

Question 18

Find the axis of symmetry for the parabola $$f(x) = (x + 4)^2$ - 8.$$

Accepted Answer

$$x = -4$$

Question 19

As $$x 	o -1^+$$, what happens to $$f(x)$$ for the rational function shown in the third image?

Accepted Answer

$$f(x) 	o +\infty$$

College Algebra Exam 3 Review: Graphing, Quadratics, & Rational Functions

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