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

Each input has exactly one output

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 $2x - 5 < 7$?

Accepted Answer

$x < 6$

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 $x^2 - 4 < 0$?

Accepted Answer

$-2 < x < 2$

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

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