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 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

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).

$0-16,750 $16,750-68,000 $68,000-137,000 $137,000-209,250 $209,250-373,650 $373,650> 10% $1675+15% $9362.50+25% $36,687.50+28% $46,833.50+33% $101,085.50+35% $0 $16,750 $68,000 $137,300 $209,250 $373,650 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: a.

𝑥 − 3 = 9 b.

2𝑥 − 4 = 8 c.

𝑥 2 − 5𝑥 = 6 d.

𝑥 − 3 = −9

Assignment Pg. 209-212 #10&11 #14 #19-21 all #34-35 #43, 45, 48,