Graphing Piecewise and Absolute Value Functions (Grades 11-12)
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Graphing Piecewise and Absolute Value Functions
Instructions:
If applicable, when graphing make sure to use open and closed circles to indicate whether the end of a line segment includes the final point or not.
Ensure all graphs are properly labeled.
1.
Graph: [math]y=5| x-3| -4[/math]
2.
Graph [math]y = 3 |2x+4| - 6[/math] . Label the vertex and the x- and y-intercepts.
3.
Graph the function [math]f(x) = -2 \ | -2x |[/math].
4.
Graph the following piecewise function.
[math]f(x) = { {:(-3",", \ \ x<-2), (0",", \ \ -2<=x<=1), (3",", \ \ x>1):} [/math]
[math]f(x) = { {:(-3",", \ \ x<-2), (0",", \ \ -2<=x<=1), (3",", \ \ x>1):} [/math]
5.
Graph the following piecewise function.
[math] f(x) = { {:(x+5",",\ \ x<-2),(-2x+3",", \ \ x>=-2):} [/math]
[math] f(x) = { {:(x+5",",\ \ x<-2),(-2x+3",", \ \ x>=-2):} [/math]
6.
Graph the following piecewise function.
[math] f(x) = { {:(-2x+1",", \ \ x<=2),(4x-4",", \ \ x>2):} [/math]
[math] f(x) = { {:(-2x+1",", \ \ x<=2),(4x-4",", \ \ x>2):} [/math]
7.
The floor function is a step function which can be represented as [math]f(x) = |_ x _| [/math]. The domain of this function is [math]RR[/math] and the range is [math]ZZ[/math]. For every input value [math]x[/math], it gives the largest integer less than or equal to [math]x[/math]. For example, [math]f(1.5) = 1[/math]. Graph this function.
8.
The ceiling function is a step function which can be represented as [math]f(x) = |~ x ~| [/math]. The domain of this function is [math]RR[/math] and the range is [math]ZZ[/math]. For every input value [math]x[/math], it gives the smallest integer greater than or equal to [math]x[/math]. For example, [math]f(-3.5) = -3[/math]. Graph this function.
9.
Graph the following function.
[math]f(x) = { {:(x+8",", \ \ x<-4), ( | \ x \ |",", \ \ -4 <= x <=4), (-x+8",", \ \ x >4):}[/math]
[math]f(x) = { {:(x+8",", \ \ x<-4), ( | \ x \ |",", \ \ -4 <= x <=4), (-x+8",", \ \ x >4):}[/math]
10.
Graph the following function.
[math]f(x) = { {:(2",", \ \ -6 <= x < -4), (- 1/4 x^2 + 6",", \ \ -4 <= x <= 2), (|x-1|+4",", \ \ 2 < x <= 6):}[/math]
[math]f(x) = { {:(2",", \ \ -6 <= x < -4), (- 1/4 x^2 + 6",", \ \ -4 <= x <= 2), (|x-1|+4",", \ \ 2 < x <= 6):}[/math]
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