Question 1

Solve for $$w in $$the equation:

$$\displaystyle \frac{2}{11}w + \frac{9}{3} = \frac{7}{w}$$

Accepted Answer

$$w = 1,\ w = 7$$

Question 2

Solve the inequality and express the solution in interval notation:

$$3(n - 5) \geq 2 + 4(n - 3)$$

Accepted Answer

$$[10, \infty)$$

Question 3

Given the points $$P(-3, 3)$$ and $$Q(6, -1)$$, what is the equation of the line in slope-intercept form that passes through both points?

Accepted Answer

$$y = -\frac{4}{9}x + \frac{1}{3}$$

Question 4

Find the standard form of the equation of the circle that passes through $$P(-3, 3)$$ and $$Q(6, -1)$$ and whose diameter is the distance between them.

Accepted Answer

$$(x - 1.5)^2$ + (y - 1)^2$ = 21.25$$

Question 5

Express the equation $$x^2$$ + $$y^2 + 5x - 5y = 40$ in standard form by completing the square.

Accepted Answer

$$(x + 2.5)^2$ + (y - 2.5)^2$ = 66.25$$

Question 6

What are the center and radius of the circle given by $$x^2$$ + $$y^2 + 5x - 5y = 40$?

Accepted Answer

Center: $$(-2.5, 2.5)$$, Radius: $$\sqrt{66.25}$$

Question 7

Simplify $$\dfrac{4 + 3i}{3 - 5i}$$ and write your answer in $$a + bi$$ form.

Accepted Answer

$$-\frac{7}{17} + \frac{29}{17}i$$

Question 8

Let $$f(x) = 2x^2$ - 3x + 2$$ and $$g(x) = 20 - x. $$Compute $$(f \circ g)(-2).$$

Accepted Answer

$$2(22)^2 - 3(22) + 2 = 2(484) - 66 + 2 = 968 - 66 + 2 = 904$

Question 9

Find the domain of $$\dfrac{f(x)}{g(x)}$$ where $$f(x) = 2x^2$ - 3x + 2$$ and $$g(x) = 20 - x.$$

Accepted Answer

$$(-\infty, 20) \cup (20, \infty)$$

Question 10

Given the function $$f(x) = \dfrac{3x - 2}{x - 3}$$, find the inverse $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \dfrac{3x + 2}{x - 3}$$

Question 11

A function $$f is $$graphed and passes the horizontal line test. Which of the following is true?

Accepted Answer

The function is one-to-one and has an inverse.

Question 12

Solve for $$x in $$the inequality $$\dfrac{3x - 5}{4} \geq 6$$ and express your answer in interval notation.

Accepted Answer

$$[9, \infty)$$

Question 13

Given $$f(x) = 2x^2$ - 3x + 2$$, compute the difference quotient $$\dfrac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$4x + 2h - 3$$

Question 14

Which of the following best describes the transformation from $$f(x) to$$ $$g(x) = -f(x-1) + 2$$?

Accepted Answer

Shift right 1, reflect over x-axis, shift up 2

Question 15

If $$f(x) is a $$function with domain $$[ -3, 4 ]$$ and range $$[ 0, 5 ]$$, what is the domain and range of $$f^{-1}(x$$)$$?

Accepted Answer

Domain: $$[0, 5]$$, Range: $$[-3, 4]$$

Question 16

Solve for $$x in $$the equation $$\dfrac{5}{6}x - 3 \leq x - 6$$ and express your answer in interval notation.

Accepted Answer

Question 17

Calculate the distance between the points $$P(-3, 3)$$ and $$Q(6, -1).$$

Accepted Answer

$$\sqrt{85}$$

Question 18

Find the midpoint $$M of $$the segment joining $$P(-3, 3)$$ and $$Q(6, -1).$$

Accepted Answer

$$(1.5, 1)$$

Question 19

Which of the following is the $$y-$$intercept of the circle $$x^2$$ + $$y^2 + 5x - 5y = 40$?

Accepted Answer

$$y = 5.5$$ and $$y = -7.5$$

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