Power Function with Modeling

Precalculus

Functions and Graphs

Chapter 2Section 2

Power Function with Modeling

Essential Question: How are power function used to specify the proportional relationships

of “real-world” problems?

Student Objectives:The student will learn write power functions with variations.

The student will learn how to write and graph monomial functions.

The student will learn how to graph power functions.

The student will learn how to use models of power functions to solve “real-world” problems.

Terms:

Constant of variation

Constant proportion

Direct variation

Inverse variation

Monomial function

Power

Power function

Proportional

Varies

Graphing Calculator Skills:

The student is expect to understand how to change the graphing window to show the

major shape of the graph.

Theorems and Definitions

Power Function

Any function can be written in the form

is a power function. The constant is the power, and is the constant of

variation, or constant of proportion. We say varies as the power

of , or is proportional to the power of x.

Sample Questions:

1.Write the power function for the statement:

The circumference varies directly as the radius.

2.Write the power function for the statement:

The volume of the gas is inversely proportional to the pressure.

3.Write the power function for the statement:

The force of the object is inversely proportional to the square of the distance

traveled.

4.Write the power function for the statement:

The stopping distance is directly proportional to the square of the speed.

5.Graph the function given below and then answer the question to complete the summary

of the power function.

a.Domain:a. ______

b.Range:b. ______

c.Continuous interval:c. ______

d.Increasing interval:d. ______

e.Decreasing interval:e. ______

f.Symmetry:f. ______

g.Bounded:g. ______

h.Relative minimum:h. ______

.iRelative maximum:i. ______

j.Horizontal Asymptotes:j. ______

k.Vertical asymptotes:k. ______

l.End behavior:l.

6.Graph the function given below and then answer the question to complete the summary