Functions
What is a function in algebra?
A function is basically an equation that has a variable that appears by itself on one side of the equation with one or more variables on the other side.
Here are two examples of what they (functions) look like:
1) y = 3x - 2
2) h = 5x + 4y
I will use the first sample given above to teach a very simple but interesting concept.
In the function, y = 3x - 2, the variable y represents the function of whatever appears on the other side of the equation. In other words, y is a function of the variable x in y = 3x - 2.
What does it mean to evaluate a function?
To evaluate a function means to pick different values for x in order to find the value of y. In terms of evaluation, for every choice of x that you pick, only ONE corresponding value of y will be the end result.
What is the difference between independent and dependent variables?
One variable depends on your selection of different numbers to have a SPECIFIC value; the other variable does NOT depend on the number or value you select. For example, in y = 4x - 2, the value of y will depend on which numbers I decide to plug in for x in the function. I will do one sample.
If x = 3, solve for y: y = 4x - 2.
y = 4(3) - 2
y = 12 - 2
y = 10
Here we can see that y became 10 when I plugged 3 for x in the function given. This means that y depended on my choice for x to become the value of 10. In other words, y depends on the choice for x but x does NOT depend on the value of y. We can now understand that y is the dependent variable and x is the independent variable.
It is also important to know that the letter y is a shorthand expression for the function notation f(x) read: "f of x" or "function of x." In other words, y = f(x) and f(x) = y. They are interchangeable. For example, y = 6x - 3 can also be written f(x) = 6x - 3.
Keep in mind that you can also use ANY LETTER to represent a function. Using the sample above, we can write f(x) = 6x -3 this way: g(x) = 6x -3, h(x) = 6x - 3, etc. This means that you can replace f with any letter of the alphabet to represent a function.
What about polynomial functions? Polynomial functions are functions that can be written when combining coefficients, variables and exponents. Here is a small list of what polynomials look like:
1) 10x
2) 6x
3) x
Remember that in terms of functions, coefficients are the constants (any real number) and the variables are the letters and exponents that MUST be whole numbers.
By Guido Feliz, Jr
(c) 2005
