Question 1

Which of the following numbers is a pure imaginary number?

Accepted Answer

$$3i$$

Question 2

What is the standard form of the complex number $$\sqrt{-48}$$?

Accepted Answer

$$4i\sqrt{3}$$

Question 3

If $$a+bi$$ and $$c+di$$ are complex numbers, which of the following is the correct formula for their product?

Accepted Answer

$$(ac-bd) + (ad+bc)i$$

Question 4

Which of the following best describes the solution set of the equation $$x^2 = -25$?

Accepted Answer

$$x = \pm 5i$$

Question 5

Given the quadratic equation $$2x^2 - x + 1 = 0$, what is the value of its discriminant and what does it indicate about the solutions?

Accepted Answer

Discriminant is $$-7$$, indicating two nonreal complex solutions.

Question 6

Which of the following is the correct process for completing the square for $$ax^2 + bx + c = 0$?

Accepted Answer

Divide by $$a$$, move $$c to $$the other side, add $$(\frac{b}{2a})^2$ to both sides, factor, then solve using the square root property.

Question 7

Which of the following intervals describes where the function $$f(x) in $$the provided graph is increasing?

Accepted Answer

$$(-2, 1)$$

Question 8

What is the slope of the line passing through the points $$(5, -3)$$ and $$(-2, -3)$$?

Accepted Answer

$$0$$

Question 9

Which of the following best describes the graph of $$f(x) = x^2$?

Accepted Answer

A parabola opening upward with vertex at $$(0,0)$$

Question 10

If $$f(x) = 2x^2$ - 3x$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$4x + 2h - 3$$

Question 11

Which of the following is the correct formula for the vertex of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

Vertex at $$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$

Question 12

Which of the following statements about the slopes of lines is true?

Accepted Answer

A vertical line has an undefined slope.

Question 13

Given the function $$f(x) = |2x + 1| \u003c 7$$, what is the solution set?

Accepted Answer

$$-4 \u003c x \u003c 3$$

Question 14

Which of the following is the correct formula for the sum of two functions $$f$$ and $$g$$?

Accepted Answer

$$(f+g)(x) = f(x) + g(x)$$

Question 15

If $$f(x) = x^3$ and g(x$$) = \sqrt[3]{x}$$, which of the following is true about their relationship?

Accepted Answer

$$g is $$the inverse of $$f$$

Question 16

Which of the following is the correct formula for compound interest compounded $$n$$ times per year?

Accepted Answer

$$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$

Question 17

Which of the following is the correct formula for the composition $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = f(g(x))$$

Question 18

If $$f(x) = 2x + 5$$, what is the equation of its inverse?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 19

Which of the following is a correct statement about the graph of $$f(x) = |x|$$?

Accepted Answer

It is a V-shaped graph with vertex at $$(0,0)$$

Key Concepts in Complex Numbers, Completing the Square, and Slopes of Lines

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