92.121(201) Management Precalculus

Spring 2012

Exam 1

Name:

Show all your work.

1. Find the domain and range of each function. Use inequality and interval notation.

a) ( ) 3 9f x x= +

b) 2( ) 1g x x= −

2. Make a table of the values for the given function and then plot the points to graph the

function by hand. 3( ) 2f x x= −

3. A company charting its profits notices that the relationship between the number of

units sold x and the profit P is linear. If 300 units sold results in $4650 profit and 375

units results in $9000 profit, find the marginal profit, which is the rate of change of the

profit. Write the equation of the profit function.

4. Find the difference quotient ( ) ( )f x h f x

h

+ − for the function: 2( ) 2 6 11f x x x= + − .

5. The resident population of Florida (in thousands) is given in the following table. Let x

equal the number of years after 1980 and y equal the number of thousands of residents.

a) Find the linear model that is the best fit for this data.

b) Is linear equation a reasonable model for this data? Explain.

c) What is the population for 2002 with your model?

Years Population(thousands)

1980 9746

1985 11,351

1990 12,938

1995 14,180

1996 14,425

1997 14,677

1998 14,916

6. Solve the system of equation algebraically and graphically.

2 3 9

2

x y

x y

+ =− − = −

7. A computer manufacturer has a new product with daily total revenue given by R = 565x

and daily total cost given by C= 6000 + 325x. How many units per day must be produced

and sold to give break even for the product? Find its y-coordinate and explain what does

it mean.

8. Solve the equation for x algebraically.

a) 5(2x +1) + 5 = 5(x – 2)

b) 5 1

4 2 3

x x

x

−+ = +

9. Write the equation of the line that passes through the point (4, 5) and perpendicular to

the line with equation 3 1

2 2y x

−

= − .