algebra 2 problem

Question

Could some one answer this please.
Write the function whose graph is the graph of y = |x|, but is vertically stretched by a factor of 8

Answer 1

When you vertically stretch a function by a certain factor, you simply multiply it by that factor.

 

So y = |x| would become y = 8|x|.

 

What does this look like?  "| |" means absolute value, which means take any negative values of the expression inside the | | and make them positive.

 

So, when x ≥ 0, |x| doesn't change x, so the y = |x| is the same as y = x.  But when x < 0, |x| DOES change x into -x -- because you have to take the negative of a negative number to make it positive.

 

So now we know what y = |x| looks like.

 

To stretch it, just multiply it by 8.  So for x ≥ 0, y = 8|x| is the same as y = 8x.  For x < 0, y = |x| is the same as y = -8x.

 

So draw the line y = 8x to the right of the y-axis, and draw y = -8x to the left of the y-axis, and you'll see what the graph looks like.