Question 1

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

Accepted Answer

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

Question 2

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

$$x = 131$$

Question 3

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

Accepted Answer

$$y = 10676.5$$, which represents the revenue and cost at break-even

Question 4

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

Accepted Answer

$$(-\infty, 7]$$

Question 5

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

Accepted Answer

$$P(x) = 7x - 1343$$

Question 6

For the profit function $$P(x) = 7x - 1343$$, what does the rate of change represent?

Accepted Answer

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

Question 7

How many units must be produced and sold to avoid a loss for the profit function $$P(x) = 7x - 1343$$?

Accepted Answer

$$x = 192$$

Question 8

Given the inequality $$-\frac{2}{3}(x-3) \u003e \frac{x}{3} + 1$$, what is the solution for $$x$$?

Accepted Answer

$$x \u003c 0$$

Question 9

Find the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 3 - 2x - x^2$ and simplify.

Accepted Answer

$$-2 - 2x - h$$

Question 10

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

Accepted Answer

$$x = 1, y = 2$$

Question 11

Given the data: Year (1998, 2000, 2002, 2004, 2006, 2008, 2010), Smoking (%) (27.0, 25.8, 25.0, 24.9, 25.1, 25.4, 24.9), what is the best linear model for $$y$$, the percent of smokers, as a function of $$x$$, years after 1985?

Accepted Answer

$$y = -0.144x + 29.2$$

Question 12

For the model $$y = -0.144x + 29.2$$, what does the slope represent?

Accepted Answer

The percent of smokers decreases by $$0.144$$ per year after 1985

Question 13

Using the model $$y = -0.144x + 29.2$$, estimate the percent of US residents smoking in 2025.

Accepted Answer

$$y = 16.16$$

Question 14

Which of the following is the equation of a vertical line passing through the point $$(5, -7)$$?

Accepted Answer

$$x = 5$$

Question 15

Which of the following is the equation of a horizontal line passing through the point $$(9, 15)$$?

Accepted Answer

$$y = 15$$

Question 16

Suppose a company’s cost function is $$C(x) = 58.5x + 2829$$ and revenue function is $$R(x) = 81.5x. $$What is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 23x - 2829$$

Question 17

If the function $$f(x) is $$defined by the graph with points $$(-3,1)$$, $$(-2,2)$$, $$(1,-2)$$, and $$(3,3) ($$open circle), what is the domain of $$f(x)$$?

Accepted Answer

$$[-3, 3)$$

Question 18

Given the same graph, what is the range of $$f(x)$$?

Accepted Answer

$$[-2, 3)$$

College Algebra Exam I – Step-by-Step Study Guidance

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