SOLUTION: Graph the follwing functions: e) y= |-5x| and y= 5|x|

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Question 155784: Graph the follwing functions:

e) y= |-5x| and y= 5|x|
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, lets graph y=abs%28-5x%29. Remember, we can break abs%28-5x%29 into -5x and -%28-5x%29=5x


So first graph y=-5x


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-5x%29 Graph of y=-5x


Now graph y=5x


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C5x%29 Graph of y=5x


Together, they look like this:



graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-5x%2C5x%29 Graph of y=-5x (red) and graph of y=5x (green)

Now because the sign outside the absolute value is positive (ie there is no sign), this tells us to only draw the upper portion like this:



graph%28500%2C500%2C-10%2C10%2C-8%2C12%2Cabs%28-5x%29%29 Graph of y=abs%28-5x%29


Now let's graph y=5%2Aabs%28x%29. To do this, first graph abs%28x%29 (which is simply a "v" shaped graph):


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2Cabs%28x%29%29 Graph of y=abs%28x%29


Now vertically stretch the graph by a factor of 5 to get the graph of y=5%2Aabs%28x%29


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C5%2Aabs%28x%29%29 Graph of y=5%2Aabs%28x%29


Notice that if you graph the two equations together you get



graph%28500%2C500%2C-10%2C10%2C-8%2C12%2Cabs%28-5x%29%2C5%2Aabs%28x%29%29 Graph of y=abs%28-5x%29 (red) Graph of y=5%2Aabs%28x%29 (green)


So this means that the two graphs are identical (since one is right on top of the other)