Absolute Value Inequalities
Vertices/End Behavior
Piecewise Functions
Pos/Neg/Increase/Decrease
Find Slope/Y-Intercept
100
|2x-7| >= -1
Solve for x, place on a number line.
x>= 3 or x<=4
100
State the vertex
(2,3)
100
f(x) = 5x-1, if x< 2
f(x) = x+3 if x>2
Solve when x = -3
f(-3) = -16
100
State on what interval the function is negative
(1,5)
100
What is the slope and y-intercept of Table 1?
Slope = 4
y-intercept = 4
200
| 5x+2 | < -4
Solve for x and place on a number line
No Solution
200
Describe the end behavior
x > infinity f(x) > infinity
x> - infinity f(x) > infinity
200
f(x) = -x +4, if x < 1
f(x) = 3 ,if -1<=x < 2
f(x) = 2x-5, if x>=2
Solve when x = 2
F(2) = -1
200
State on what interval the function is descreasing.
x<3
200
What is the slope and y-intercept of Table 2?
Slope = 6
Y-intercept = 4
300
|6x-7| -8 >= 3
Solve and put into interval notation
(-infinity, -2/3] u [3, infinity)
300
State the vertex
(-3,-4)
300
f(x) = -x if x <2
f(x) = x-6 if x>=2
Solve when x = -100
f(-100) = 100
300
State on what intervals the function is positive.
( -infinity,5) n (5,infinity)
300
What two tables represent linear functions?
Table A and Table B
Slope Table A and B = -2
400
3|14-x|> 18
Solve and put on number line
x>20 or x<8
400
What is this absolute value function called?
Parent Function
400
f(x) = 2x+1 if x<= -1
f(x) = -x+2 if -1< x < 2
f(x) = -3 if x>=2
Solve when x = 0
f(0) = 2
400
For what x values is the function increasing?
x > 5
400
Find the slope and y-intercept then put into slope-intercept form.
m = 2 b = 8
y = 2x+8
500
6|1/4x+3| +7 > 7
x< 12 or x>12
500
Describe the end behavior
x> infinity f(x) > - infinity
x > - infinity f(x) > -infinity
500
f(x) = 55x if 0<=x<=2
f(x) = 65x-20 if 2<x<=5
Solve when x = 4
f(4) = 240
500
For what x values is the function decreasing, and for what x values is the function increasing?
Decrease x < 0
Increase x > 0
500
Interpret the slope.
For every 1 hour, 55 miles is traveled.