1. MAT 150 – Algebra Class #10 Topics: Evaluate and graph piecewise-defined functions Graph absolute functions Solve absolute value equations

2. 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.

3. Evaluating and Graphing a Piecewise- Defined Function a.Evaluate f(-2), f(-1) and f(.5) b.Graph the given piecewise- defined function.

4. 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 isOf the Amount over $0-16,75010%$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?

5. 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.

6. Solving Absolute Values

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