Question 1

Simplify and write the following complex number in standard form: $$\frac{1 + 7i}{8 + 2i}$$

Accepted Answer

$$\frac{3}{34} + \frac{27}{34}i$$

Question 2

Solve the rational inequality and write the solution set in interval notation: $$\frac{x-4}{x+5} \leq 0$$

Accepted Answer

$$(-5, 4]$$

Question 3

Given the points $$A(-2, 3)$$, $$B(4, -1)$$, plot these points on the provided coordinate plane and find the distance between them.

Accepted Answer

$$\sqrt{36 + 16} = 2\sqrt{13}$$

Question 4

Complete the table for the equation $$y = 2x + 1.$$

Accepted Answer

For $$x = -2, y = -3$$; $$x = 0, y = 1$$; $$x = 2, y = 5$$

Question 5

Which graph best represents the function $$f(x) = \sqrt{x + 6}$$?

Accepted Answer

Graph 1 (first graph with curve starting at $$x = -6)$$

Question 6

Find the slope of the line passing through the points $$(-1, 3)$$ and $$(3, -2).$$

Accepted Answer

$$m = -\frac{5}{4}$$

Question 7

Determine if the relation $$\{(0,3),(-2,6),(5,1),(0,8)\} is a $$function and if it is one-to-one.

Accepted Answer

It is not a function.

Question 8

Given $$f(x) = x^2$ + 11$$ and $$g(x) = x + 4$$, find $$(f-g)(1).$$

Accepted Answer

$$(f-g)(1) = 8$$

Question 9

For the quadratic function $$h(x) = x^2$ - 10x + 25$$, what are the coordinates of the vertex?

Accepted Answer

$$(5, 0)$$

Question 10

Solve the exponential equation: $$2(9)^{3x} = 13122$

Accepted Answer

$$x = 2$$

Question 11

Convert the logarithmic equation $$y = \log_6$(216) to $$exponential form and solve for $$y.$$

Accepted Answer

$$6^y = 216$$, so $$y = 3$$

Question 12

Solve the absolute value equation $$|2x - 5| = 9.$$

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 13

Which of the following best describes the function $$g(x) = 4x^3$ - x$$?

Accepted Answer

Odd function

Question 14

Find the center and radius of the circle given by the equation $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$.

Accepted Answer

Center $$(3, -4)$$, radius $$2$$

Question 15

Evaluate the exponential function $$g(x) = 3$$^{-x+2}$$ at x = 1$.

Accepted Answer

$$g(1) = 3$$

Question 16

Solve the logarithmic equation $$\log(5x) = 4.$$

Accepted Answer

$$x = 2000$$

Question 17

Which of the following is the correct interval notation for the solution set of $$|x - 3| \u003c 5$$?

Accepted Answer

$$( -2, 8 )$$

Question 18

Given $$f(x) = 2x^2$ + 4$$, what is the y-intercept?

Accepted Answer

$$(0, 4)$$

Question 19

For the polynomial $$g(x) = x^3$ - 3x^2$ - 13x + 15$$, which of the following is a rational zero?

Accepted Answer

$$x = 5$$

Guidance for Rational Inequality and Complex Number Division

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