Function Operations Help

Subject Areas

Tools / Misc

bCalc

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scrnGC2: Calc Input

scrnGC3: f(x) Plot Input

scrnGC4: g(x) Plot Input

The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.

gCalc

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Select precision* of answer:

Select angle mode:

Enter expression to evaluate here:

The answer is shown below:

Enter function to be plotted:

f(x) =

Enter 2nd function, if needed:

g(x) =

Change or reset the x-y scaling below:

x_min =

x_max =

y_min =

y_max =

Accuracy Disclaimer

The javascript math object methods used for this calculator are not accurate for very large or very small numbers. In particular, the trigonometric functions may yield very small answers that should actually be zero or very large answers that should be infinite. This typically occurs at 90� or pi/2 intervals.

DO NOT USE WHERE HIGH PRECISION IS REQUIRED. USE AT YOUR OWN RISK.

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Function Operations Help

Evaluating a Function

Many functions use x as the independent variable and y or f(x) as the dependent variable. Evaluation of a function is as simple as substituting the given number in every position that it appears in the function, as shown below:

Example 1:
Given: f(x) = x� + 2x -3; f(-2)=?

Step 1:  f(     ) = (    )� + 2 (    ) - 3
Step 2:  f(-2) = ( -2 )� + 2 ( -2 ) - 3
Step 3:  f(-2) = 4 - 4 - 3 = -3,

Rewrite the given function, replacing each "x" with a set of parenthesis. In the example at the left, -2 is placed in each placeholder position since the function is to be evaluated for x = -2. Compute the answer following the order of operations.

Although f(x) is commonly used to express a function, any other notation can be encountered; i.e. g(m) is the function g having m as its independent variable.

Adding Functions

When two functions are added together, it is simple matter of adding similar terms.

Example 2:
Given: f(x) = x� + 2x -3
g(x) = 3x� + 4x +5
f(x) + g(x)= 4x� + 4x + 2

Generally, polynomials are written from highest degree to lowest degree, from left to right. In this example, the highest degree is x�. Adding the x�terms from both functions results in 4x�. Adding the next term, x results in 6x. Adding the constant terms, results in a +2. The sum is therefore;
4x� + 4x + 2.

Subtracting Functions

When two functions are subtracted, change the sign of all the terms being subtracted and proceed as in addition.

Example 3:
Given: f(x) = 5x� + 2x -4
g(x) = 2x� + 3x +5
f(x) - g(x) = ?

Solution:
          f(x) = 5x� + 2x -4
        -g(x) = -2x� - 3x -5
f(x) - g(x) =  3x� - x - 9

Multiplying Functions

When two functions are multiplied, use generic rectangles (as shown in earlier) or use FOIL.

Example 4:
Given: f(x) = 2x -3
g(x) = 3x +5
f(x) * g(x) = ?

Solution:
f(x) * g(x)
(2x -3)*(3x +5) = 6x� + x - 15

Dividing Functions

When two functions are divided, the solution is the first function divided by the second unless the two functions share a common factor. The main thing that you have to watch for is when the denominator goes to zero. Setting the denominator to zero and solving will give you the number in the domain where the function is undefined.

Example 5:
Given: f(x) = 3x -2
g(x) = 3x +5
f(x) / g(x) = ?

Solution:
          f(x) / g(x)
          (3x - 2)/(3x +5) = (3x - 2)/(3x +5);  x  ≠  -5/3
          Note that 3x+5 cannot equal zero.