Why is U = 3?

[jade zinc]

I don't understand why U is 3 and ChatGPT can't explain it that well.

I also don't understand how to solve these questions and no luck on youtube or anything of sorts.

[snow ginkgo]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[buoyant thunder]

the corner of f(x) is at (0,3) from plotting the transformed version of |x|

so the image of f is (-inf,3]

[jade zinc]

I don't understand

[broken quartz]

It’s saying what is the range of the function

Or more specifically what set of numbers does the function map the reals to

So we see that there is no minimum value

As increase x and our number becomes more negative

However since you are always subtracting a positive amount

The maximum that function can be is when x is zero ao your subtracting nothing

Leaving just three

This is the function mapping an x onto a y

@jade zinc

[jade zinc]

oh I see

how would I work this out for future questions like this

[broken quartz]

Well you have to just look

See if any numbers cannot be made

For example a quadratic say x^2 we know it’s minimum is 0

So it maps all real numbers from 0 to infinity

It can be zero so that’s a closed set, and obviously infinity is an open set as that’s not a value it can take

[jade zinc]

Thanks for the explanation 👍🏼

Sadly I don't really understand this topic it seems

Do you reccomened any good youtube videos to get a better understanding?

I also noticed by trying a few of these questions that if the question is something like " 8 - 5x" putting in the constant which is 8 in this case is right all the time. Not sure if that is just a coincidence or if I can just keep doing that for these types of questions