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 $$x  0$$?

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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