Q: For the company above, what is the y-coordinate of the break-even point, and what does it represent?

$$R(121) = 81.5 \times 121 = 9841.5. It $$represents the total revenue and cost at break-even.

Q: Using the model $$y = -0.15x + 27$$, estimate the percent of U.S. residents smoking in 2025.

$$y = -0.15 \times 40 + 27 = 21$$

Question 1

Given the graph shown, what is the domain of the function?

Accepted Answer

$$[-3, 3)$$

Question 2

Given the graph shown, what is the range of the function?

Accepted Answer

$$[-2, 3)$$

Question 3

A company produces and sells a wireless doorbell with revenue $$R(x) = 81.5x$$ and cost $$C(x) = 58.5x + 2829$$, where $$x is $$the number of units sold. What is the break-even number of units?

Accepted Answer

$$121$$

Question 4

For the company above, what is the y-coordinate of the break-even point, and what does it represent?

Accepted Answer

$$R(121) = 81.5 	imes 121 = 9841.5. It $$represents the total revenue and cost at break-even.

Question 5

For the function $$f(x) = 7 - x^2$, what is the domain?

Accepted Answer

$$(-\infty, \infty)$$

Question 6

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

Accepted Answer

$$(-\infty, 7]$$

Question 7

Given the table of U.S. smoking rates, which model best fits the data for $$y$$, the percent of smokers, as a function of $$x$$, years after 1985?

Accepted Answer

$$y = -0.15x + 27$$

Question 8

What does the slope of the model $$y = -0.15x + 27$$ represent in the context of U.S. smoking rates?

Accepted Answer

The average decrease in smoking percentage per year after 1985.

Question 9

Using the model $$y = -0.15x + 27$$, estimate the percent of U.S. residents smoking in 2025.

Accepted Answer

$$y = -0.15 	imes 40 + 27 = 21$$

Question 10

A company’s profit from 232 units is $$321, and from 264 units is 545. $$What is the equation of the profit function?

Accepted Answer

$$P(x) = 7x - 1333$$

Question 11

For the profit function $$P(x) = 7x - 1333$$, what does the rate of change represent?

Accepted Answer

The profit increases by $7 for each additional unit sold.

Question 12

How many units must be produced and sold to avoid a loss for $$P(x) = 7x - 1333$$?

Accepted Answer

$$191$$

Question 13

Solve the inequality $$-23x - 3 \u003e x^3$ + 1$$ for $$x.$$

Accepted Answer

$$x \u003c -1$$

Question 14

Find the difference quotient for $$f(x) = 3 - 2x - x^2$ and simplify.

Accepted Answer

$$\frac{-2h - 2xh - h^2$}{h}$$

Question 15

Solve the system by elimination: $$3x - 6y = -9$$ and $$9x = 15 - 3y.$$

Accepted Answer

$$x = 0, y = 1.5$$

Question 16

What is the equation of the vertical line passing through $$(5, -7)$$?

Accepted Answer

$$x = 5$$

Question 17

What is the equation of the horizontal line passing through $$(9, 15)$$?

Accepted Answer

$$y = 15$$

College Algebra Exam I – Domain and Range from a Graph

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