Q: A retailer sells appliances according to the model $$N(t) = 72t + 125$$, where $$t is $$the number of years since opening. How many appliances were sold in 2017 if the store opened in 2010?

$$N(7) = 72 \times 7 + 125 = 629$$

Question 1

Given the relation $$\{(2,3), (1,0), (-4,-5), (2,-3)\}$$, what is the range of the relation?

Accepted Answer

$$\{3, 0, -5, -3\}$$

Question 2

Which of the following relations is a function?

Accepted Answer

$$\{(0,1), (1,2), (2,3)\}$$

Question 3

Given the function $$f(x) = -x^2$ + 7$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 7]$$

Question 4

If $$f(x) = -x^2$ - 3$$, what is $$f(-2)$$?

Accepted Answer

$$1$$

Question 5

Which of the following graphs represents a function?

Accepted Answer

A graph where every $$x$$ value corresponds to exactly one $$y$$ value

Question 6

Find the slope of the line passing through the points $$(1, 5)$$ and $$(3, 1).$$

Accepted Answer

$$-2$$

Question 7

What is the equation of the line passing through $$(2, 4)$$ with slope $$-3 in $$slope-intercept form?

Accepted Answer

$$y = -3x + 10$$

Question 8

Find the $$x-$$intercept of the equation $$5x + 4y = 20.$$

Accepted Answer

$$(4, 0)$$

Question 9

A retailer sells appliances according to the model $$N(t) = 72t + 125$$, where $$t is $$the number of years since opening. How many appliances were sold in 2017 if the store opened in 2010?

Accepted Answer

$$N(7) = 72 	imes 7 + 125 = 629$$

Question 10

Given the linear model $$y = 13x + 29$$ for the number of ebook downloads (in hundreds) from 2015 to 2019, what is the predicted number of downloads in 2022?

Accepted Answer

$$y = 13 	imes 7 + 29 = 120$$

Question 11

If the price of a gallon of milk is modeled by $$P(t) = 2.35(1.02)^t$$, where $$t is $$the number of years since 2005, what is the approximate price in 2013?

Accepted Answer

$$P(8) = 2.35(1.02)^8$ \approx 2.73$$

Question 12

Which of the following best describes the rate of change in the model $$N(t) = 72t + 125$$?

Accepted Answer

The number of appliances sold increases by 72 each year

Question 13

Given the equation $$2x - 3y = 12$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, 4)$$

Question 14

A line passes through $$(2,1)$$ and is perpendicular to the line $$y = 3x + 2. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -\frac{1}{3}x + \frac{5}{3}$$

Question 15

If a function $$f(x)$$ passes the vertical line test, which of the following must be true?

Accepted Answer

Each $$x$$ value corresponds to exactly one $$y$$ value

Question 16

Given the equation $$x = 1.5$$, what type of line does this represent?

Accepted Answer

A vertical line

Question 17

If the $$x-$$intercept of a line is $$(3, 0)$$ and the $$y-$$intercept is $$(0, -2)$$, what is the equation of the line in standard form?

Accepted Answer

$$2x - 3y = 6$$

Question 18

A graph of a quadratic function opens downward and has a vertex at $$(0,7). $$What is the domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 7]$$

Question 19

If the slope of a line is $$0$$, what can you conclude about the line?

Accepted Answer

It is a horizontal line

College Algebra Study Notes: Functions, Graphs, and Linear Equations

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