Essential Skills Chapter 4

1. Identifying properties of linear functions Section 4.1

Example: If ,

a) Determine the slope and y-intercept of f.

b) Use the slope and y-intercept to graph f.

c) Determine the average rate of change of f on the interval

d) Determine whether f is increasing, decreasing, or constant.

Answers: a) , b) start at , then go down three and right two to

c) d) decreasing

2. Using linear functions as models Section 4.1

Example: In 2002, major league baseball signed a labor agreement with the players. In this agreement, any team whose payroll exceeds $128 million starting in 2005 will have to pay a luxury tax of 22.5% (for first-time offenses). The linear function describes the luxury tax T of a team whose payroll is p (in millions of dollars).

a) What is the implied domain of this function?

b) What is the luxury tax for a team whose payroll is is $160 million?

c) What is the payroll of a team that pays a luxury tax of $11.7 million?

Answers: a) b) $7.2 million c) $180 million

3. Graphing quadratic functions Section 4.3

Example: Sketch the graph of . Label the vertex and y-intercept.

Answer:

2. 4. Finding optimal values of quadratic models Section 4.3

Example: Paradise Travel Agency’s monthly profit P (in thousands of dollars) depends on the amount of money x (in thousands of dollars) spent on

advertising per month according to the rule . What is Paradise’s maximum monthly profit?

Answer: $15,000

5. Constructing and using quadratic models Section 4.4

Example: A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side

along the highway, what is the largest area that can be enclosed?

Answer: 500,000 square meters