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# HELP!!! C3 modulus function graphs I'm very confused:(( watch

1. Okay guys, I'm really confused to the answer of q4b, why is it a reflection in the y axis?? And why is the shape symmetrical?? I would've thought the left side of the axis (for negative values of X) would be more of a shape similar to the original but a reflection in the X axis as we are considering the modulus of the function . And why are the coordinates of X 1 and -1 shouldn't it be 1 and -3/2 (if you multiply eveything by sf 1/2) ??

Edit: the question is asking for f(|2X|) just to clarify as it looks a bit blurred
2. Note that:

Therefore for:
x = -1, f(|x|) = f(|-1|) = f(1),

x= -2, f(|-2|) = f(2),

etc.

Can you see why we have a symmetric graph?
3. (Original post by simon0)
Note that:

Therefore for:
x = -1, f(|x|) = f(|-1|) = f(1),

x= -2, f(|-2|) = f(2),

etc.

Can you see why we have a symmetric graph?

Yes thank you! It's because all the X values in the negatives will have the same y values as to the ones on the positives so it's a reflection in the Y axis? but now I'm confused on why y=|f(x)| is reflected in the X axis ? What is the difference between them two ? I'm getting mixed up 😢😢
...It's because all the X values in the negatives will have the y value as to the ones on the positives so it's a reflection in the Y axis?
Yes.

...but now I'm confused on why y=|f(x)| is reflected in the X axis ? What is the difference between them two ?
There is a difference between f(|x|) and |f(x)|.

Note |a| is the "absolute value" of a, so we are only interested in the value of a rather than the sign of a.

For f(|x|), f takes the absolute value of x.
(So f(|-2|) = f(2), f(|5|) = f(5) ).

For |f(x)|, this is the absolute value of y.
5. Compare the following for f(x) = sin(x).

- sin(|x|)
Note we take the sin of the absolute value of x, f can still be negative:

Attached Images

6. (Original post by simon0)
Yes.

There is a difference between f(|x|) and |f(x)|.

Note |a| is the "absolute value" of a, so we are only interested in the value of a rather than the sign of a.

For f(|x|), f takes the absolute value of x.
(So f(|-2|) = f(2), f(|5|) = f(5).

For |f(x)|, this is the absolute value of y.
Thank youuuuu😭💕 So are you saying with |f(x)| you work out the y value as its dependent on x then you take the modulus, which will tell you the absolute value of y but with f(|x|) we want the absolute value of x so we take the modulus of that only, modulus measures the magnitude so all X will be positive which is essentially why the graph is a reflection as mentioned before, Is my understanding correct? Also is this anyway related to graph transformations like the y=-f(X) and y=f(-X) ?
7. (Original post by simon0)
Compare the following for f(x) = sin(x).

- sin(|x|)
Note we take the sin of the absolute value of x, f can still be negative:

I'm confused on the last one, why is it still a negative even after we've taken the modulus
8. - |f(x)| = |sin(x) |
Note here we take the absolute value of sin(x).

So here negative values of sin(x) are taken to be positive.

So:

Attached Images

I'm confused on the last one, why is it still a negative even after we've taken the modulus
The function is: sin(|x|).

We are told here to take the absolute value of x, that is all.

-----------------------------------------------------------

In this case:

Therefore

(Note, different from: , as
Therefore ).

Can you see the difference now? :-)
10. (Original post by simon0)
The function is: sin(|x|).

We are told here to take the absolute value of x, that is all.

-----------------------------------------------------------

In this case: .

Therefore

Can you see the difference now? :-)
Thank you ever so much! I can finally sleep in peace
Thank youuuuu😭💕 So are you saying with |f(x)| you work out the y value as its dependent on x then you take the modulus, which will tell you the absolute value of y but with f(|x|) we want the absolute value of x so we take the modulus of that only, modulus measures the magnitude so all X will be positive which is essentially why the graph is a reflection as mentioned before, Is my understanding correct?
Yes.

Also is this anyway related to graph transformations like the y=-f(X) and y=f(-X) ?
Similar concept in regards that "f(-x)" and "-f(x)" are different.

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