2.7+Use+Absolute+Value+Functions+and+Transformations

** Absolute Value Functions: **
★ You can define an absolute value function, f(x)=/x /. ☆ The highest or lowest point on the graph of an absolute value function is the vertex.

__Here's a link that may help to explain things:__

[|Absolute Value Functions]



** Transformations: **
Stretches, shrinks, and refelctions: When /a/ does not equal 1, the graph of y= a/x/ is a vertical stretch or a vertical shrink of the graph y= /x/, depending on whether /a/ is less than or greater than 1. The graph of y=a*f(x-h) + k can be obtained from the graph of any function y=f(x) by perfroming these steps:


 * Step 1 ** Stretch or shrink the graph of y= f(x) vertically by a factor of /a/ if function /a/ does not equal 1. If /a/ > 1, stretch the graph. If /a/ < 1, shrink the graph.
 * Step 2 ** Reflect the resulting graph from Step 1 in the x- axis if a < 0.
 * Step 3 ** Translate the resulting graph from Step 2 horizontally //h// units and vertically //k// units.

[|Transformations]

[|How To Graph an Absolute Value Function]

★ You can derive new absolute value functions from the parent function through transformations of the parent graph. ☆ Transformation changes a graph's size, shape, position, or orientation. ★ Translation is a transformation that shifts the graph horizontally and/or vertically, but doesn't change size, shape, or orientation. ☆ Precise functions can be defines by at least 2 equations. ★ Reflection is a transformation that flips a graph or figure in a line. a=1; a<0 but a is not = -1. Reflection is a vertical stretch/shrink with x-axis reflection.

__Here's a video if you need anymore help:__

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Example Problem 1: Graphing Functions
Y= |x| -7 First plot the points on the graph by substituting in numbers for x. We will start off with a negative number to plug into x. Y=|-5|-7 5 -7 = -2 so your first coordinate will be (-5,-2) Now you just go down the list of numbers. Y=|-4|-7 4-7= -3 (-4,-3) Y=|-3|-7 3-7= -4 (-3,-4) Y= |-2|-7 2-7=-5 ( -2, -5) As you can see the last and first coordinates are flipped which is what will create the V shaped graph. Then you simply plot the points and then you are done.
 * ~Remember, any negative number put into x turns into a positive number unless there is a negative sign outside of the absolute value itself, like so : y= - |x| -7. **

[|All the notes for 2.7]