##### Notes

This printable supports Common Core Mathematics Standard HSF-IF.C.7b, HSF-IF.C.7

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# 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: $y=5| x-3| -4$ 2.
Graph $y = 3 |2x+4| - 6$ . Label the vertex and the x- and y-intercepts. 3.
Graph the function $f(x) = -2 \ | -2x |$. 4.
Graph the following piecewise function.
$f(x) = { {:(-3",", \ \ x<-2), (0",", \ \ -2<=x<=1), (3",", \ \ x>1):}$ 5.
Graph the following piecewise function.
$f(x) = { {:(x+5",",\ \ x<-2),(-2x+3",", \ \ x>=-2):}$ 6.
Graph the following piecewise function.
$f(x) = { {:(-2x+1",", \ \ x<=2),(4x-4",", \ \ x>2):}$ 7.
The floor function is a step function which can be represented as $f(x) = |_ x _|$. The domain of this function is $RR$ and the range is $ZZ$. For every input value $x$, it gives the largest integer less than or equal to $x$. For example, $f(1.5) = 1$. Graph this function. 8.
The ceiling function is a step function which can be represented as $f(x) = |~ x ~|$. The domain of this function is $RR$ and the range is $ZZ$. For every input value $x$, it gives the smallest integer greater than or equal to $x$. For example, $f(-3.5) = -3$. Graph this function. 9.
Graph the following function.
$f(x) = { {:(x+8",", \ \ x<-4), ( | \ x \ |",", \ \ -4 <= x <=4), (-x+8",", \ \ x >4):}$ 10.
Graph the following function.
$f(x) = { {:(2",", \ \ -6 <= x < -4), (- 1/4 x^2 + 6",", \ \ -4 <= x <= 2), (|x-1|+4",", \ \ 2 < x <= 6):}$         You need to be a HelpTeaching.com member to access free printables.