Question 1

Find the distance between the points $$A = (5, 3)$$ and $$B = (7, 7). $$Give an exact answer, and where appropriate, an approximation to three decimal places.

Accepted Answer

$$\sqrt{20}, 4.472$$

Question 2

Which of the following is the equation of a circle with center at $$(4, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 4)^2$ + (y + 2)^2$ = 25$$

Question 3

Find the center and radius of the circle given by $$x^2$$ + $$y^2 - 6x + 8y = 0$.

Accepted Answer

Center: $$(3, -4)$$, radius: $$5$$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1, 2), (2, 3), (1, 5)\}$$

Question 5

Find the domain of the function $$f(x) = \dfrac{4x}{x^2$ - 16}.$$

Accepted Answer

All real numbers except $$x = 4$$ and $$x = -4$$

Question 6

Given $$f(x) = x^2$ + 5x$$, find $$f(-3).$$

Accepted Answer

$$-4$$

Question 7

Find the slope of the line containing the points $$(1, 4)$$ and $$(7, -4).$$

Accepted Answer

$$-\dfrac{4}{3}$$

Question 8

Find the slope and $$y-$$intercept of the equation $$12x + 9y = 45.$$

Accepted Answer

Slope: $$-\dfrac{4}{3}$$, $$y-$$intercept: $$5$$

Question 9

Write a slope-intercept equation for a line with slope $$\dfrac{2}{3}$$ passing through $$(0, 5).$$

Accepted Answer

$$y = \dfrac{2}{3}x + 5$$

Question 10

Determine whether the pair of lines $$8x - 6y = 6$$ and $$4x - 3y = 6$$ are parallel, perpendicular, or neither.

Accepted Answer

Parallel

Question 11

Solve the equation $$9x - (2x - 1) = 22.$$

Accepted Answer

$$x = \dfrac{11}{7}$$

Question 12

Solve the inequality and graph the solution set: $$|x + 2| \u003c 9.$$

Accepted Answer

$$(-11, 7)$$

Question 13

Given the relation $$\{(-7, 6), (-7, -3), (0, 7), (8, -7), (8, 7)\}$$, is this relation a function?

Accepted Answer

No

Question 14

Given $$f(x) = 4x^2$ + 2x$$, find $$f(3).$$

Accepted Answer

$$42$$

Question 15

Given $$g(h) = 12h^2$ + 28h - 3h^3$, find g(2$$)$$.

Accepted Answer

$$29$$

Question 16

Find the domain of the function $$f(x) = \dfrac{3x - 2}{x^2$ - 18}.$$

Accepted Answer

All real numbers except $$x = \sqrt{18}$$ and $$x = -\sqrt{18}$$

Question 17

Find the domain and range of the function represented by the graph of $$y = -x + 3$$ for $$x in$$ $$[0, 3].$$

Accepted Answer

Domain: $$[0, 3]$$, Range: $$[0, 3]$$

Question 18

Given the function $$f(x) = x^2$ - 2x - 3$$, find the $$x-$$intercepts.

Accepted Answer

$$x = -1, 3$$

Question 19

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h in $$feet after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. $$What is the maximum height reached by the ball?

Accepted Answer

$$32 ft$$

Precalculus Review: Distance, Circles, Functions, Lines, and Inequalities

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