Question 1

Which of the following is the correct definition of the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 2

What is the result of multiplying $$3 + 2i$$ and $$1 - 4i$$?

Accepted Answer

$$11 - 10i$$

Question 3

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 4

Solve the quadratic equation $$x^2 - 6x + 9 = 0$.

Accepted Answer

$$x = 3 ($$double root)

Question 5

Which of the following best describes the discriminant of a quadratic equation $$ax^2 + bx + c = 0$?

Accepted Answer

$$b^2 - 4ac$

Question 6

A ball is thrown upward with an initial velocity of $$20 m/s $$from a height of $$2$$ meters. Its height $$h$$ after $$t$$ seconds is given by $$h = -4.9t^2$ + 20t + 2. $$After how many seconds does the ball hit the ground?

Accepted Answer

$$t = 4.2$$ seconds

Question 7

Which of the following is NOT a function?

Accepted Answer

Some inputs have more than one output

Question 8

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 9

Which of the following intervals represents the solution to the inequality $$2x - 5 \u003c 7$$?

Accepted Answer

$$x \u003c 6$$

Question 10

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$(f \circ g)(2) = 9$$

Question 11

Which of the following best describes the range of the function $$f(x) = \sqrt{x - 3}$$?

Accepted Answer

$$[0, \infty)$$

Question 12

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$P = 18$$ thousand dollars

Question 13

Which of the following is the solution set for $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5, x = -2$$

Question 14

Which of the following statements is true about the graph of a function that passes the vertical line test?

Accepted Answer

Each input has exactly one output

Question 15

Solve for $$x$$: $$\frac{2x + 3}{x - 1} = 5$$

Accepted Answer

$$x = 2$$

Question 16

Which of the following is the correct solution to the equation $$x^2 + 4x + 8 = 0$?

Accepted Answer

$$x = -2 \pm 2i$$

Question 17

If the domain of a function $$f is$$ $$[2, \infty)$$, which of the following could be the function?

Accepted Answer

$$f(x) = \sqrt{x - 2}$$

Question 18

Which of the following best describes the solution to the system of equations: $$x + y = 5$$ and $$x - y = 1$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 19

Which of the following is the correct solution to the inequality $$x^2 - 4$$ \u003c 0$$?

Accepted Answer

$$-2 \u003c x \u003c 2$$

Question 20

If $$f(x) = 3x - 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{3}$$

College Algebra Unit Test 1 Review: Key Concepts and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard