relations and functions question

[john252]

I'm trying to solve the math problem above. So far I put the 0 and 1 in the boxes and that turned out to be correct, but I can't figure out how to find what goes in all of the other boxes and what the f(x) is. I don't know what steps I am supposed to do to find the answers. Thanks for reading.

 

[Dr.Peterson]

You are told to cube the input, x, to make the output, y.

When x is 0, you cubed it and got 0 (because [imath]0^3=0\times 0\times 0 = 0[/imath]).

When x is 1, you cubed it and got 1 (because [imath]1^3=1\times 1\times 1 = 1[/imath]).

What do you get when you cube 2?

What expression do you write when you cube x? That will be what f(x) is.

If you need a better understanding of functions and the related notation, you might start here:

What is a Function

www.mathsisfun.com

 

[JeffM]

A function relate one thing to another unambiguously.

If a function named f relates a number x to number z, we say f(x) = z.

Functions are often defined by a mathematical formula.

[math]f(x) = x^3[/math]
means that we are relating the number x, whatever that is, to its cube.

 

[john252]

Thank you JeffM and Peterson for helping me out. I finally got the answers after using your advice to multiply each number by it's cube of 3.

 

[HallsofIvy]

I don't understand what you mean by "multiply each number by its cube of three"! The "cube of three" is 3*3*3= 27 and you did NOT multiply each number by 27! I suspect that your "cube of three" just meant the third power but that is what "cube" means! And you do not "multiply" by it.

What you did was "cube each number". That was exactly what this problem told you to do:
"Cube the input, x".

 

[Dr.Peterson]

Thank you JeffM and Peterson for helping me out. I finally got the answers after using your advice to multiply each number by it's cube of 3.

The problem itself used the correct terminology. If you want to paraphrase to show your understanding, another way to say "cube each number" would be "raise each number to the third power".

 

[Steven G]

You are told to cube the input, x, to make the output, y.
To make means equal. 7 + 2 makes 9 or 7+2 = 9, for example.

Cube the input x, means x^3. To make the output y means = y.
So cube the input, x, to make the output, y,
means x^3 = y or y=x^3.