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### Course: Integrated math 3>Unit 6

Lesson 4: Scaling functions

# Identifying horizontal squash from graph

Given the graphs of functions f and g, where g is the result of compressing f by a factor of 2, Sal finds g(x) in terms of f(x).

## Want to join the conversation?

• I really don't get this... what is the difference between vertical vs horizontal stretching/contracting? When I see a trasformed function, I just can't decide in which 'direction' it has been modified... it could well be both!
• Vertical is up and down and horizontal is side to side so you just have to visualize what would happen to something if it was stretched in that directions. I usually think about people.

If I took you, and stretched you vertically (i.e. in an up and down direction) you would look taller and skinnier - something we could all hope for.. However, if I stretched you horizontally (i.e. side-to-side) you would get shorter and fatter.

Hope my crazy explanation is helpful.
• what is the difference between 2f(x) and f(2x)?
• 2f(x) says to multiply the function values by 2.
So, let's say the function is f(x) = x^3 + 4x - 2,
If we then chose x to be 5,
f(5) would equal 125 + 20 -2 = 143
and 2f(5) would equal 286
However f(2x) says to double the value that is used as input,
so f(2x) would be f(10)
which would become 1000 +40 - 2 = 1038 (--- nowhere near 286!)
To summarise,
having 2f(x) merely doubles the output figures.
Having f(2x) doubles the input figures and, depending on the function, that input may also then be raised to a power, multiplied by a constant, scaled down by a fraction, etc.
Hope you find this useful!
• Can someone please provide me with an explanation of what "in terms of" means, I understand the mathematics but whenever a question has "in terms of x, etc." I struggle to understand what to do?

Thanks
• When a question asks for "in terms of x", it just means that "x" appears in the answer. You might want to think of it as "using x". If the question asks for "g(x) in terms of f(x)", it means that you will be using f, although it might not literally be "f(x)". It might be something like "g(x) = 2 f(x - 1) + 3". But if you are given a relationship between g(x) and f(x), and you are asked to give g(x) in terms of x, then your answer should not mention f.
• Shouldn't g(x) = f(x/2) though?
• No.
For example, 𝑥 = −2 ⇒ 𝑔(𝑥) = 𝑔(−2) ≈ 1.8,
while 𝑓(𝑥∕2) = 𝑓(−1) ≈ 3
1.8 ≠ 3, so at least for 𝑥 = −2, we have 𝑔(𝑥) ≠ 𝑓(𝑥∕2)
• How do you tell the difference between graphs that have been scaled kf(x) vs. graphs that have been scaled f(kx)?
• kf(x): The entire function is scalled by "k". For example, if f(x) = x^2+3 then kf(x) = kx^2 +3k

f(kx): All terms involving "x" will now also include the "k". For example, if f(x) = x^2+3, then f(kx) = (kx)^2+3
Notice, the "k" is also squared in the first term, and the 3 did not change.

Hope this helps.
• Hi , correct me if i'm wrong but I think that g(x) = 1/2f(x) is also true because if I substitute (x) with one of it's values f(2) for exemple I get g(x) = 1/2f(2) which equals to 1 in the graph. and g(x) is found in terms of f(x) , thanks.
• g(2) would not = 1/2 f(2)
1/2 f(2) = 1/2 * 1/2 = 1/4
Yet, g(2) = -4, not 1/4
So, your strategy is not working.

Notice: Sal is defining when f(x) = g(x) based on their input values. What input values create the same output values.
Sal came up with f(x) = g(x/2)
You would also say f(2x) = g(x)
Hope this helps.
• How come g(x)=f(2x) instead of a g(x)=1/2f(x)?
• `g(x) = f(2x)` is saying that `g(x)` is half as wide as `f(x)`, because for any `x` in `g(x)`, it will be the same `y` value as `f(x)` when you double `x`.

`g(x) = 1/2 f(x)` is saying that `g(x)` is half as tall as `f(x)`, because for any `y` which is an output of `f(x)`, `g(x)` will out put a `y` value half as large.
• How would you expand expand g(x) to get f(x)?
• For expanding a function u have to multiply the function with a number smaller than 1 and larger than 0 . It will decrease the slope of the function(for a given input of (x) you will have a smaller output of (y) )
(1 vote)
• Is compression and reflecting the same thing?