The graph of a function is horizontally compressed by a factor of 5 and vertically compressed by a factor of 2 Find an equation for this compressed function in terms of the function f(x)

Question

The graph of a function  is horizontally compressed by a factor of 5  and vertically compressed by a factor of 2 Find an equation for this compressed function in terms of the function f(x)

whpalmer4 · Answer

Horizontal compression means that the value of x given to the function grows faster than x.  So, if your function = 0 at x = 0, and 4 at x = 2, compressing it by a factor of 2 horizontally would make the function = 0 at x = 0, and 4 at x = 1.  A little thought should show that this is the same as writing f(2*x) or f(2x).  Now how about the vertical compression?  Do we want to multiply, or divide, by our scale factor?

anonymous · Answer

i thought the answer was y=2f(5x)
but it comes back as wrong im not sure whats is wrong. i know the a=vertical b=horizontal

whpalmer4 · Answer

Ah, but you're *compressing* the vertical scale, right?  Is that multiplying by 2, or dividing by 2?

anonymous · Answer

divide?

whpalmer4 · Answer

You tell me.  Say your function is f(x) = x^2.  

x     y = x^2 y = 2x^2    y = 1/2 x^2
0           0              0               0
1           1               2             1/2
2           4               8             2
3           9               18           4 1/2

which one of those looks like it is y = x^2 vertically compressed by a factor of 2?

anonymous · Answer

the last one

whpalmer4 · Answer

Right, for vertical compression, we divide by the compression factor.  So your answer to the problem is?

anonymous · Answer

1/2f(5x)