algebra 2 problem

Question

I'm kind of stumped with this problem here.  Write the function whose graph is the graph of y=|x|but is vertically stretched by a factor of 3. I don’t understand what y equals in this case

Answer 1

Either

y = 3| x |

or 

y = | 3x |

 

Graph these two on the same plane with 

 

y = | x | to see the "stretch."

Answer 2

The graph of y=|x| looks like a "V" with the point at the origin (0,0).  The absolute value is always positive and it is equal to the magnitude of x.  It always has a positive value.

 

"Vertically stretched" means multiplied by 3.  If you stretch something that is 1 foot long to become 3 times its length, it is 3 units long.  And an object initially 2 units long becomes 6 unites long.

 

So, the new function is also in the shape of a "V" but somewhat skinnier (this is really fun to do to someone's photo using Photoshop).  Three times is far worse than Barbie, however.   Also note:  they used to use ropes to tie people to wheels to "stretch" them.

 

As a kid, my brother (always 3 years older, so you could say, HisAge=MyAge+3) came home from school and wanted to play "Stretch."  We took a big knife, stood 3 feet apart facing each other, and threw the knife into the ground -- you're out if you hit a foot and it didn't count if it didn't stick or it was more than a knife's length away; but otherwise he must "stretch" to move his foot to the position of the knife.  When you can't "stretch" (thus, fall down), you lose.  Oh -- and you both lose when mom can't find her big cutting knife and comes to check on you (DON'T TRY THIS AT HOME!)