# Thread: Horizontal Stretch and Shrink

1. ## Horizontal Stretch and Shrink

Could someone explain to me how this works? I get perfectly how Vertical works but i'm having some trouble with this one

y= f(4x) and y=f(1/4x)

thanks

2. It's not a trick. You just have to play with it until it soaks in.

Look at f(x).

What will f(4x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f(4(1/4)) = f(1)
If you want f(4), you must put in f(4(1)) = f(4)

What will f((1/4)x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f((1/4)4) = f(1)
If you want f(4), you must put in f((1/4)16) = f(4)

One way to think about it, anyway.

3. Originally Posted by TKHunny
It's not a trick. You just have to play with it until it soaks in.

Look at f(x).

What will f(4x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f(4(1/4)) = f(1)
If you want f(4), you must put in f(4(1)) = f(4)

What will f((1/4)x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f((1/4)4) = f(1)
If you want f(4), you must put in f((1/4)16) = f(4)

One way to think about it, anyway.

So basically when 0 < c < 1, then it is stretching which means getting closer to the x-axis? When c > 1 then it is shrinking which means it is getting further away from the x-axis.

Also isn't horizontal at all similar to vertical stretch and shrink? Sorry i'm not understanding at all why the division is there. Can someone else explain it to me in an easier sense.... much appreciated

4. help someone?

5. Originally Posted by TKHunny
It's not a trick. You just have to play with it until it soaks in.

Look at f(x).

What will f(4x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f(4(1/4)) = f(1)
If you want f(4), you must put in f(4(1)) = f(4)

What will f((1/4)x) do? 'f' does the same thing, but it now takes a different input value to get it to do the same thing.

If you want f(1), you must put in f((1/4)4) = f(1)
If you want f(4), you must put in f((1/4)16) = f(4)

One way to think about it, anyway.

If graphed, f(4x) would be further away from the x-axis thus making it shrink. f((1/4)x) would in turn stretch. So basically is it the opposite of the Vertical Stretch and Shrink rules?

c > 1 then stretches and 0 < c < 1 means to shrink

6. Originally Posted by JonathanEyoon
If graphed, f(4x) would be further away from the x-axis thus making it shrink. f((1/4)x) would in turn stretch. So basically is it the opposite of the Vertical Stretch and Shrink rules?

c > 1 then stretches and 0 < c < 1 means to shrink
the other way around, yes

7. Originally Posted by Jhevon
the other way around, yes

The problem that i'm doing with instructions is

Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph f.

a) y = f(4x) and b) y = f((1/4)x)

for part a) it would be, the graph is horizontally shrinking by 4 and part b) the graph is horizontally stretching by 1/4.

Am I correct? If not could you explain. Thanks~

8. Originally Posted by JonathanEyoon
The problem that i'm doing with instructions is

Suppose the graph of f is given. Describe how the graph of each function can be obtained from the graph f.

a) y = f(4x) and b) y = f((1/4)x)

for part a) it would be, the graph is horizontally shrinking by 4 and part b) the graph is horizontally stretching by 1/4.

Am I correct? If not could you explain. Thanks~
you have the idea i believe.

rephrase: (a) f(4x) is obtain by horizontally compressing f(x) by a factor of 4

...............(b) f((1/4)x) is obtained by horizontally stretching the graph of f(x) by a factor of 4

Note, particularly, that we stretch it by a factor of 4, not 1/4, when we have f(1/4)x)

9. Originally Posted by Jhevon
you have the idea i believe.

rephrase: (a) f(4x) is obtain by horizontally compressing f(x) by a factor of 4

...............(b) f((1/4)x) is obtained by horizontally stretching the graph of f(x) by a factor of 4

Note, particularly, that we stretch it by a factor of 4, not 1/4, when we have f(1/4)x)

wait i'm confused again haha.... the answer in the back of the book claims that f(4x) is shrinked by 1/4 while f((1/4)x) is stretched by 4.

two questions :

Why does the book say 1/4 for the first one and why is it 4 for the second one?

10. Originally Posted by JonathanEyoon
wait i'm confused again haha.... the answer in the back of the book claims that f(4x) is shrinked by 1/4 while f((1/4)x) is stretched by 4.

two questions :

Why does the book say 1/4 for the first one and why is it 4 for the second one?
its the same thing. shrinked by 1/4 or shrinked/compressed by a factor of 4, they mean the same thing.

i just think the latter sounds better

11. Originally Posted by Jhevon
its the same thing. shrinked by 1/4 or shrinked/compressed by a factor of 4, they mean the same thing.

i just think the latter sounds better

ok so then why is the second one stretched by 4 and not 1/4?

12. Originally Posted by JonathanEyoon
ok so then why is the second one stretched by 4 and not 1/4?
the graph will be stretched horizontally so that its horizontal length on any finite interval will be 4 times what it was originally, stretching by a factor of 4 is the way we would describe that. if we say we stretched it by 1/4, that means it only increased by 1/4 of its original length as opposed to 4 times its original length

13. Originally Posted by Jhevon
the graph will be stretched horizontally so that its horizontal length on any finite interval will be 4 times what it was originally, stretching by a factor of 4 is the way we would describe that. if we say we stretched it by 1/4, that means it only increased by 1/4 of its original length as opposed to 4 times its original length

haha I'm confused and dont' understand what you're saying. Could we work with problems?

y = f(4x) means it will shrink by 4 and y = f((1/4)x) means it will stretch by 1/4? You told me the second one will stretch by 4 and not 1/4. I'm not understanding why we use 4 and not 1/4. Sorry for being such a pain it's just i'm really needing to understand this stuff

14. Originally Posted by JonathanEyoon
haha I'm confused and dont' understand what you're saying. Could we work with problems?

y = f(4x) means it will shrink by 4 and y = f((1/4)x) means it will stretch by 1/4? You told me the second one will stretch by 4 and not 1/4. I'm not understanding why we use 4 and not 1/4. Sorry for being such a pain it's just i'm really needing to understand this stuff
for the second, the graph stretches four times its original length on any finite interval.

think of it this way. we use our x-value as a measure of the horizontal distance traveled, right? so when we say, for example, f(1), what we are saying is, "the value of the function when we are one horizontal unit from the y-axis"

now, staying with f(1), and assume we are dealing with a function f(x) on a finite inteval. let's say we want to get to f(1) from the function f(x). well, we just plug in x = 1 and we're done.

what about f(4x). well, to get f(1), we need to plug in x = 1/4, since f(4*(1/4)) = f(1). so you see, we reach the desired value, four times as fast. no longer do we have to go all the way to 1, we can just travel to 1/4, which is 4 times LESS the distance. so f(4x) shrinks the graph by a factor of 4. or we can equivalently say, it shrunk by 1/4, to say the graph is now 1/4 of its original length

what about f((1/4)x)? to get to f(1), we need to plug in x = 4, since f((1/4)*4) = f(1). so now instead of going to 1, we have to go all the way to 4 to get the same value. so the graph stretches 4 times as long as it was, and therefore, we stretch it by a factor of 4.

15. Originally Posted by Jhevon
for the second, the graph stretches four times its original length on any finite interval.

think of it this way. we use our x-value as a measure of the horizontal distance traveled, right? so when we say, for example, f(1), what we are saying is, "the value of the function when we are one horizontal unit from the y-axis"

now, staying with f(1), and assume we are dealing with a function f(x) on a finite inteval. let's say we want to get to f(1) from the function f(x). well, we just plug in x = 1 and we're done.

what about f(4x). well, to get f(1), we need to plug in x = 1/4, since f(4*(1/4)) = f(1). so you see, we reach the desired value, four times as fast. no longer do we have to go all the way to 1, we can just travel to 1/4, which is 4 times LESS the distance. so f(4x) shrinks the graph by a factor of 4. or we can equivalently say, it shrunk by 1/4, to say the graph is now 1/4 of its original length

what about f((1/4)x)? to get to f(1), we need to plug in x = 4, since f((1/4)*4) = f(1). so now instead of going to 1, we have to go all the way to 4 to get the same value. so the graph stretches 4 times as long as it was, and therefore, we stretch it by a factor of 4.

Ok I think some things are starting to click in my brain. Question, the book doesn't specify to use f(1) but to just tell what would happen. You using f(1) and and the book not telling me to use f(1) is giving the same answer. Does this mean whenever I horizontally stretch or shrink, I should aim to try to find how much the graph stretches or shrinks by trying to make it equal to 1?

*sigh* my professor didn't explain it the way you are in the least bit. He just told us one gets closer to the x-axis and the other gets further away.

Can you by any chance you can just tell me how to do horizontal stretching and shrinking in a really easily understandable way? I feel like i'm getting more and more confused and I have my first major test on this stuff tomorrow. =/ thanks

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