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# Help. ​

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Help.

NotSoSmart  Sep 28, 2017
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Look at    -7x^2       and   -35x^2

Note that for each  x value  we put in the first function, the second function is 5 times as much

For instance if x  = 1.......    -7(1)^2  = -7

But     -35(1)^2   = -35 * 1    =   -35    ......five times as much as the first one.....

So.....

g(x)  "stretches" f(x)  by a factor of 5

The  " +5"   at the end of the second function just translates  -35x^2  up   5 units

So

g(x)   stretches  f(x)  vertically by a factor of 5 and translates this up 5 units

y  = x  ...if we have a vertical stretch of 6 units......x  must become  6x

So       y =  6x

Look at the graph here : https://www.desmos.com/calculator/lsp6ddool2

Note that when x  = 2  in y = x....then  y = 2

But....when  x  = 2  in 6x........then y  = 12.......six times as much  !!!!

y  = x/6   =  y = (1/6) x      so this one actually vertically  "compresses"   the original function.....

y  = x + 6     just translates y = x  up 6 units

y  = x - 6     translates y  = x  down 6 units

Hang in there, NSS.....these are sometimes difficult for me, too.....!!!!!

CPhill  Sep 28, 2017

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