MAT 150 – AlgebraClass #10Topics:

• Evaluate and graph piecewise-defined functions

• Graph absolute functions

• Solve absolute value equations

Piecewise-Defined Functions

Some data cannot be modeled with a single equation. We then use what is called a piecewise-defined function to represent the situation. A piecewise-defined function is so named because it is defined with different pieces for different parts of its domain rather than one equation.

Evaluating and Graphing a Piecewise-Defined Function

a. Evaluate f(-2), f(-1) and f(.5)

b. Graph the given piecewise-defined function.

Creating a Piecewise-Defined Function The 2010 U.S. federal income

tax owed by a marred couple filing jointly can be found from the following table.

If Taxable Income Is Between

Tax Due is Of the Amount over

$0-16,750 10% $0

$16,750-68,000 $1675+15% $16,750

$68,000-137,000 $9362.50+25% $68,000

$137,000-209,250 $36,687.50+28% $137,300

$209,250-373,650 $46,833.50+33% $209,250

$373,650> $101,085.50+35% $373,650

Questions

a. Write the piece-wise defined function T with input x that models the federal tax dollars owed as a p function of x, the taxable income dollars earned, with 0 < x < 137,300.

b. Use the function to find T(42,000).

c. Find the tax owed on a taxable income of $65, 000.

d. A friend tells Jack Waddell not to earn anything over $68,000 because it would raise his tax rate to %25 on all of his taxable income. Test this statement by finding the tax on $68,000 and $68,000 + $1. What do you conclude?

Solving Absolute Value Equations

Absolute value function is a piecewise-defined function.

The absolute value of a number is never negative, we cannot solve |x| = a if a is negative.

Solving Absolute Values Solve the following equations:

Assignment

Pg. 209-212

#10&11

#14

#19-21 all

#34-35

#43, 45, 48,