Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 2

Given the relation $\{(1, 1), (2, 4), (3, 9), (4, 16), (5, 25)\}$, what is the range?

Accepted Answer

$\{1, 4, 9, 16, 25\}$

Question 3

Which equation below does NOT define a function?

Accepted Answer

$x + y^2 = 3$

Question 4

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

Accepted Answer

$11$

Question 5

Which of the following is the general form of a linear function?

Accepted Answer

$f(x) = ax + b$

Question 6

A line passes through the points $(2, 1)$ and $(8, 5)$. What is its slope?

Accepted Answer

$\frac{2}{3}$

Question 7

Which quadrant contains points where $x < 0$ and $y > 0$?

Accepted Answer

Quadrant II

Question 8

What is the equation of the line passing through $(3, -1)$ with slope $4$?

Accepted Answer

$y + 1 = 4(x - 3)$

Question 9

If a machine is purchased for $8000 and has a salvage value of $500$ after $10$ years, assuming linear depreciation, what is the annual rate of depreciation?

Accepted Answer

$750$

Question 10

Given the depreciation function $V(t) = -750t + 8000$, what is the value of the machine after $7$ years?

Accepted Answer

$2750$

Question 11

Which of the following lines is parallel to the line $y = 2x + 5$?

Accepted Answer

$y = 2x - 3$

Question 12

Two lines are perpendicular if their slopes $m_1$ and $m_2$ satisfy which condition?

Accepted Answer

$m_1 m_2 = -1$

Question 13

What is the equation of the vertical line passing through $(3, 5)$?

Accepted Answer

$x = 3$

Question 14

If the cost $y$ of buying $x$ bubble teas is modeled by $y = 3x + 5$, what is the cost for $6$ bubble teas?

Accepted Answer

$23$

Question 15

Which of the following statements about the slope of a linear function is TRUE?

Accepted Answer

The slope represents the constant rate of change of the function.

Question 16

What is the y-intercept of the line $2x - 3y = 12$?

Accepted Answer

$-4$

Question 17

Solve the equation $7x - 4 = 3x + 8$ for $x$.

Accepted Answer

$3$

Question 18

Which of the following is NOT a property of equality used to solve equations?

Accepted Answer

Dividing both sides by zero preserves equality.

Question 19

If a line has slope $0$, what type of line is it?

Accepted Answer

Horizontal line

Question 20

A business purchases equipment for $12,000$ and expects it to be worthless after $8$ years. What is the linear depreciation function $V(t)$ for $0 \leq t \leq 8$?

Accepted Answer

$V(t) = -1500t + 12000$

Linear Functions and Equations in Business Calculus

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