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Theory

With a formula such as y = - x 3 + 4 x you will find exactly one value for y for every value of x . In that case, y is a function of x with function rule y ( x ) = - x 3 + 4 x .

When you are given a function, you can compute a table and draw the corresponding graph. The values of the input variable are found on the horizontal axis, the x -axis.
The results are called function values.
y ( 1 ) = - 1 3 + 4 1 = 3 is the function value if x = 1 . Function values are found on the -axis.

You also find the expression f ( x ) being used for y ( x ) . y then is a function of x that is given the name f .
In contextual situations you often use letters that have some connection to the meaning or name of the variable. For time you use t , for length you use l , for volume you use V , for velocity you use v , for power you use P , etc. Your graphing calculator is set to use X as the standard input variable, and Y as the standard function value.

The zeros or roots of a function are those input values that give you a function value of 0 . For the function above these are the -values for which:
y ( x ) = - x 3 + 4 x = 0 .
In this case these values are x = 0 , x = 2 and x = -2 .
The corresponding x-intersects are ( 0 , 0 ) , ( -2 , 0 ) and ( 2 , 0 ) .

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