Question

Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch.
f(x)=√(x)
g(x)=8√(x)

Answer 1

it will stretch vertically by 8 units. there are the rules of transformations of graphs. want me to write all of them down??

Answer 2

yes please :)

Answer 3

wait no, i got confused, it would shrink horizontally by 1/8 units. You'll see once I write them down ;)

Answer 4

ok, so
RIGID TRANSFORMATIONS (shape does not change)
1. horizontal shift: a) to the right: f(x-c)
b) to the left f(x+c)
2. vertical shift: a) up: f(x)+c
c) down: f(x)-c
3. reflection over x: -f(x)
4. reflection over y: f(-x)

NON-RIGID TRANSFORMATIONS:(shape changes)

1. vertical stretch c>1, cf(x)
2. vertical shrink 0<c<1, cf(x)
3. horizontal stretch 0<c<1, f(cx)
4. horizontal shrink c>1, f(cx)
for the last 3 and 4 of this category, you should write it like this: horizontal ____ by 1/c units.

Answer 5

so because the 8 before the sqrt(x) it would mean that it is a vertical stretch of 8?

Answer 6

yup you're correct. I always get confused with this stuff. Im sorry haha

Answer 7

its ok :) thank you for your help