Question

The transformation from f to g represents a __________ stretch.

Answer 1

\[f(x)=\sqrt{x}\] and \[g(x)=\sqrt{0.1x}\]

Answer 2

@ranga @phi I thought this was a shrink since c<1...

Answer 3

Here is what they look like

Answer 4

To stretch or shrink the graph in the x direction, divide or multiply the input

Notice that we are multiplying x by 0.1 (or, the same thing) dividing x by 10
x/10

dividing the input by a constant *stretches the function in the x direction*

Answer 5

but is it a stretch? I know it's vertical since c is multiplied by x instead of divided by x. But the question says its a stretch but I thought if c<1, then its a shrink. Since it goes from sqrt(x) to sqrt(0.1x) and 0.1 is less than 1, wouldn't it be a shrink?

Answer 6

Here is an example of horizontal stretch (by 2) which is not quite so extreme as by x/10 (a horizontal stretch by 10)

Answer 7

It looks like the vertical (the y) has been shrunk, but what is really going on is the x is being stretched.

Answer 8

if you have f(x) a vertical stretch by 10 would by 10*f(x)
when f(x) = sqrt(x), this would mean 10*sqrt(x)

a Horizontal stretch by 10 is f(x/10) which means
sqrt(x/10)