Can someone explain mathematical functions to an advanced 7th grader???

Question

HELP! I have to take an SAT as part of a gifted program and I don't understand functions! I will really appreciate it if you can at least explain what f(x) is and what it means that it is a whole number.

Answer 1

Hello,

This might be a bit long but it includes only what you need to know plus examples.

Functions are like a black box which you give a number (or something more complex) and get something back. For example we can have a function f(x) = 2x. You are probably familiar with x, it is a variable. You can put a number in for x like 3 and the function will return 6. You simply replace x with whatever your input is and solve. So if f(x) = 2x,

f(2) = 2*2 = 4
f(3) = 2*3 = 6
f(-2) = 2*-2 = -4

Functions can get a little more complicated like f(x) = (3/x+3)^2 but they are the same idea. Just plug in whatever you need for x and solve. Here are more examples: f(x) = (3/x+3)^2 + x

f(3) = (3/3+3)^2 + 3 = (1+3)^2 + 3 = 4^2 + 3 = 19
f(6) = (3/6+3)^2 + 6 = (2+3)^2 + 6 = 5^2 + 6 = 31

The last thing you need to know is that you can plug in more than a number for x. We can replace x with another variable, a math expression, or even another function. examples

if f(x) = 2x+1:
f(a) = 2a+1
f(2a) = 2(2a)+1 = 4a+1
f(2b+2) = 2(2b+2)+1 = 4b+4+1 = 4b+5
f(2c^2) = 2(2c^2)+1 = 4c^2+1

if f(x) = 2x+1. And g(y) = y^3+5,
f(g(y)) = 2(g(y))+1 = 2(y^3+5)+1 = 2y^3+10+1 = 2y^3+11

You can make it harder by adding more mathmatical operations but the idea is the same. Remember, a function is just a representation of an operation. You can evaluate a function by replacing the variable with the input. Thats about it.

Answer 2

f(x) is math language for an equation, also known as a function, with a variable in it represented by x. For example, let's say f(x) = 10. That doesn't mean much until we find out algebra equation that f(x) represents. An example would be f(x) = 3x + 4. Putting those to together we know that 3x + 4 = 10. So now we can find out what x is, or solve for x, as they say. In this case x has to be 2 so that 3*2 + 4 will equal 10.

Answer 3

f(x) doesn't really mean much by itself.
Lets say you have f(x) = x^2 - 3x.
What you can do is let x be anything you want. f(1) is just the number you get when you put 1 into the above: 1^2 - 3*1 = -2. f(2) = 2^2-3*2 = -2. Etc.

Its just a way of writing a complicated expression.

Answer 4

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Answer 5

f(x) doesnt mean anything by itself. There has to be something like:

f(x) = 2x + 13

or f(x) = 3sin(x)

it just refers to some function of x. As the value of x changes the value of f(x) (which is just a place holder or name to use so you can talk about the fuction (e.g. 2x + 13) without having to type it out every time) also changes. Using my first function, when x=0, f(x) = 13 . when x=1 f(x) = 15.....

Answer 6

f(x) is an expression
in which u put the values
of x to find f(x)
eg.f(x)=x^2
put x=2& u get
f(x)=4
but it doesnot mean that
they are always whole no.
eg f(x)=1/x
moreover in a function
for a different value of x
u should get a unique
value of f(x)
sof(x)=x^2 is a function for all
positive real nos. i.e here
you cannot consider the
whole set of real nos.

Answer 7

K say they give you..

f(3) = 2x + 4

3 = x in this equation.
plug x in and solve.