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Absolute Value Functions!!
Day One
Should we do this later?
No, DO NOW
Complete the Absolute Value Exploration Sheet with a Pal
Hot News!
After School Help w/Mr. Meyer in the Media Center
Every Wednesday 2:15-3:00 PM
Tuesdays and Thursdays by Appointment (Send me an email or ask me the day before)
http://honorsalgebra2meyer.wikispaces.com/
Rules for Graphing Absolute Value Functions
The graph of f(x)=a*|x-h|+k has the following characteristics:
A) Vertex (h,k), symmetric with x=h
B) V-shaped, opens UP if a>0 and DOWN if a<0
C) Wider than parent function if |a|<1 and narrower than parent function if |a|>1
Graphing!
1) Find the vertex.
(1,1)
2) “a” is negative, and so, it opens downwards.
3) Find one other point on the graph. (Use the slope.)
(2,0)
4) Use symmetry to plot the point on the other side of the vertex.
Writing Equations
1) Identify the vertex.
(3,1)
2) Identify the a value.
Point (4,3) is on the graph.
3=a*|4-3|+1.
a=2
3) Substitute into y=a*|x-h|+k.
y=2*|x-3|+1
Write it Piecewise!
Write the absolute value equation as a piecewise function.
1)So if , the equation of the line is found as follows:a-Slope is -2 from the graphc-The point (2,3) is on the line. Use this to find the intercept:f(x)=-2x+b3=-2*(2)+b, b=7.
So if , the line has equation f(x)=-2x+7
Write it Piecewise
2) So if x>3, the equation of the line is found in the same way to be f(x)=2x-5.
3) Write it together as a piecewise as:
f(x)= -2x+7; (-∞, 3] 2x-5; (3, ∞)
Practice Hit “Y=“
Enter into Y1 a function of the form f(x)=a*|x-h|+k
To get absolute value, hit ‘MATH’, scroll right to ‘NUM’, and hit 1:abs(
For this exercise, pick a, h, and k (your parameters) between -5 and 5.
Hit ‘GRAPH’
Trade calculators with your partner and try to come up with the absolute value and piecewise equations for your partners graph.