Question

If K = {(x, y)|x - y = 5}, find the corresponding range of y for the domain {0, 2, 4}.


{-5, -3, -1}
{0, 2, 4}
{5, 7, 9}

Answer 1

Okay, let's translate this monstrosity into English, shall we?

What this function is saying is this:

"X and Y must match the condition that (x - y = 5)." If I recall correctly, that | symbol translates to "where".

So for every two numbers (x and y) we put into this equation, the two of them have to equal 5.

We know that our domain (X values) is (0, 2, 4), so what we'll do is plug each one in in turn, and see what comes out. This is a function, remember, so only one number can be outputted.

To input a number into a function, we replace all of our x's in a function with that number. (Or y's, if we're putting in y, or b's if we're putting in b...you get the idea.)

So K = {(x, y)|(x - y = 5)} translates to:

K = {(0, y)| (0 - y = 5)}

Okay, so how do we determine y? We solve our equation. 0 - y = 5. What does y equal? Negative 5.

Let's do our other x's a bit faster:

K = {(x, y)|(x - y = 5)}
K = {(2, y)|(2 - y = 5)}
y = -3

One more:

K = {(4, y)|(4 - y = 5)}
y = -1

So, let's tally up our y's. We have -5, -3, and -1. This leads to a range of, obviously, (-5, -3, -1), which conveniently matches up with one of our answers :)

This was a more complex question, so if I didn't explain something in enough detail, just ask and I'll give it a more detailed pass :)

Answer 2

You're my savior.

Answer 3

Again, happy to help :) That was a difficult one, I can see why you're having trouble when they're introducing new concepts so blazingly fast. 0.0

Answer 4

It's constantly a new thing! It's so much to process. /:

Answer 5

If f(x) = x 2 + 1 and g(x) = 3x + 1, find [f(4)] 2.


81
257
289
like wtf is this stuff... dear lawd...

Answer 6

That question seems...well, really odd. I think you're missing a key detail in that one.

Is that x 2 supposed to be x squared? You can show that like this: x^2. (That ^ is Shift+6 on your keyboard.)

Also, go over the question again, and see if that [f(4)] 2 is missing something.

Lastly, holy CRAP, dude, you're going from "What's the domain and range of this function" to multiple functions in the space of an hour? No wonder you're having trouble...

Answer 7

Yes it's suppose to mean x squared..

Answer 8

and the [f(4)] 2 is supposed to be [f(4)] squared..

Answer 9

Okay, so in this question, as far as I can tell, the g function is a red herring. So here's our relevant information:

f(x) = x^2 + 1.

Find f(4^2).

So what we do is, we replace every instance of "x" with "4^2", or 16 for simplicity's sake.

f(x) = x^2 + 1.
Find f(16).

See if you can get it from here; you can refer back to the last question I answered for you if you're not sure what "replacing x" means. If you can't get it, ask me in a few minutes and I'll help you with the remainder.

Answer 10

I give up on math forever... for tonight especially. I might bleed out of my eyes if I have to do anymore...

Answer 11

Okay, I probably shouldn't, but I'll have mercy and give you the calculations for this last one, then you can refer back to it when you're fresh tomorrow.

f(x) = x^2 + 1.
Find f(16).

We replace every instance of "x" with an instance of "16".

f(16) = 16^2 + 1.

16^2, as a calculator will show you, is 256.

f(16) = 256 + 1
f(16) = 257.

Good luck with functions, mate. If you're finding it too difficult, that Khan Academy link has a MUCH gentler introduction to functions than your class material appears to.