Question

Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch.
f as a function of x is equal to the square root of x and g as a function of x is equal to 3 times the square root of x

Answer 1

So the difference between
f(x)= sqrt(x) and g(x)=3sqrt(x) ?

Answer 2

Yes

Answer 3

Well, in a horizontal stretch, lets devote a letter to where that stretch would occur in a function equation. Let's pick C.
Horizontal stretch: y=f(Cx)
Vertical stretch: y= Cf(x)

Answer 4

Make some sense?

Answer 5

Yeah, that makes sense.

Answer 6

So tell me, by the sample format equations I just gave you, is the difference between the f(x) function and the g(x) function a horizontal or vertical stretch?

Answer 7

I believe it's a horizontal stretch, right?

Answer 8

Take a look at where the 3 is..
Its outside the function, therefore vertical.

Answer 9

Oh okay, yeah that makes sense. I'm sorry. I really don't understand this lesson so I appreciate you breaking it down.

Answer 10

How would you describe the transformation? Would it be shifted up 3 units?

Answer 11

@karatechopper

Answer 12

Sorry haah I got afk sometimes.
It's basically like if you get a function like g(x)=3x
Then you multiply the x constant by the 3

Answer 13

And then plot your point from there

Answer 14

We can stretch or compress it in the y-direction by multiplying the whole function by a constant.

Answer 15

If that makes more sense^

Answer 16

Yes, thank you so much

Answer 17

https://www.mathsisfun.com/data/function-grapher.php?func1=sqrt(x)&func2=2*sqrt(1*(x+1))+1&xmin=-12&xmax=12&ymin=-8&ymax=8
Play around with this graph, it might provide a better visual! and np! Welcome to OpenStudy btw! :)