Question

Can someone help me with relations and functions?

Answer 1

@studio-games

Answer 2

@ILovePuppiesLol

Answer 3

@CandyCove

Answer 4

@phi @agent0smith @IrishBoy123 @zepdrix @mathstudent55 @freckles

Answer 5

Thanks!

Answer 6

Look at the table of values.
This table shows a relation called f.

Answer 7

Okay.

Answer 8

This relation is a function, the function is called f.
What you can read from the table is this:
When x is 0, y is 1.
When x is 1, y is 3.
When x is 3, y is 7.
etc.

Answer 9

The problem is using function notation instead of using x and y.
Function notation is confusing to use at first, but it is really simple, and it gives more information than using x and y.

Answer 10

Okay, but how does that work please?

Answer 11

Let's say you have a function expressed by the equation:

y = x + 1

If I asked you, for x = 1, what is y?
You plug in 1 for x, and you get:

y = 1 + 1
y = 2

Your answer is "for x = 1, y is 2.

Ok so far?

Answer 12

I think so but still confusing, sorry.

Answer 13

Another example using the same function I wrote above.

I can then ask you:

"What is y for x = 25?"

Once again, you do

y = x + 1
y = 25 + 1
y = 26

Your answer: y = 26 for x = 25

Since I am asking to use a value of x = 25, you plug in 25 for x, and you figure out what y is for that specific value of x.

Answer 14

Now would I do the same thing for the problem I gave you at the beginning?

Answer 15

Or how would I do that type of a problem?

Answer 16

Let me just explain how function notation works with my example, then we'll go to your problem.

Now let's use function notation to see how it works.
I will still use my example equation from above.

I am calling my function function f.
In function notation, you replace y with the name of the function, in this case, f, but you write it as f(x). This is read "f of x", and it means that function f is a function of variable x.

Answer 17

In regular notation

y = x + 1

becomes

f(x) = x + 1

in function notation.

As you can see, y was replaced by the name of the function, f, but f is written as f(x).

Answer 18

Now you will see the advantage of function notation.
In the regular notation, if I want you to give me the value of the function when x = 1, I need to ask "what is y when x = 1?"

Now I can say that entire question by simply saying "what is f(1)"?
This means evaluate the function called f at x = 1.
You still plug in 1 for x like we did before, but instead of answering y is 2 when x = 1, you simply write f(1) = 2

f(1) means what is the value of the function f when x = 1.

Answer 19

Using my example function,
what is f(4)

f(x) = x + 1
f(4) means plug in 4 for x and evaluate the function
f(4) = 4 + 1
f(4) = 5

When you answer me f(4) = 5, you are saying the y value of function f is 5 when x is 4.
As you can see, it is much quicker to simply say "f4) = 5.

Answer 20

do you always just add 1 though?

Answer 21

My previous examples:

What is y when x = 1?
Now becomes: what is f(1)

f(x) = x + 1
f(1) = 1 + 1
f(1) = 2

What is y when x = 25?
Now becomes: what is f(25)?

f(x) = x + 1
f(25) = 25 + 1
f(25) = 26

Answer 22

Ok. Now (if I didn't put you to sleep yet) we can go back to your problem.
Your problem is using function notation.
There is a function called f in your problem.
We are not given an equation for function f, but we do know the value of the function at some x values.

Answer 23

From the table, you see
f(0) = 1
f(1) = 3
f(3) = ... (read in your table)

Answer 24

No you didn't put me to sleep rather kept my interested and a little confused at times.

Answer 25

I'm so dumb.

Answer 26

Thank you for all of your help!

Answer 27

Your problem's question of what is f(3) (in function notation) is the same as asking "when x is 3, what is y"?

Answer 28

Okay.

Answer 29

You're welcome.
You're not dumb.
Dumb would be not knowing and not asking questions.
Not knowing but asking questions is smart.

Answer 30

Okay well thank you anyways! I also fanned and meadled you. Even thought that isn't a word.

Answer 31

If you have any other questions, fell free to tag me anytime. I'll try to answer your questions.

Answer 32

Thanks, and you're welcome.