MAT 150 – Algebra
Class #10
Topics:
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 PiecewiseDefined Function
a. Evaluate f(-2), f(-1) and f(.5)
b. Graph the given piecewisedefined 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,