Function Table Calculator

How to Use the Function Table Calculator

This guide will help you understand how to use the Function Table Calculator, which generates a table of function values and other related calculations for specific mathematical functions. Follow the steps below to input your values and view the results.

Step 1: Enter Input Values

• Start X Value:

  In this field, enter the starting X value for your table. This value must be a number between -1000 and 1000, with increments of 0.1. Ensure this field is filled, as it is required.

• End X Value:

  Enter the ending X value for your table in this field. Similar to the Start X Value, this must be a number between -1000 and 1000, and you must fill this field.

• Step Size:

  Provide the step size in this field. The step size determines the intervals at which the function will be calculated between the start and end X values. It must be between 0.1 and 100.

• Function Type:

  Select the type of function you wish to calculate from the dropdown menu. Options include:

  • Linear (ax + b)
  • Quadratic (ax² + bx + c)
  • Cubic (ax³ + bx² + cx + d)
  • Exponential (a * eˣ)

Step 2: View the Results

Once you have entered all the required input values and selected a function type, the calculator will generate a table with the following results:

• X Value:

  This column displays the X values starting from the specified Start X Value and increments by the specified Step Size until the End X Value is reached.

• Y Value:

  For each X value, the corresponding Y value is calculated based on the selected function type using the formula:

  • Linear: (2 times text{X value} + 1)
  • Quadratic: ((text{X value}^2 + 2 times text{X value} + 1))
  • Cubic: ((text{X value}^3 + text{X value}))
  • Exponential: (e^{text{X value}})
• Derivative at X:

  This column indicates the derivative of the function at each X value:

  • Linear: 2
  • Quadratic: (2 times text{X value} + 2)
  • Cubic: (3 times text{X value}^2 + 1)
  • Exponential: (e^{text{X value}})
• Definite Integral:

  This field displays the definite integral from Start X to End X of the selected function type:

  • Linear: ((2 times text{endX}^2/2 + text{endX} – (2 times text{startX}^2/2 + text{startX})))
  • Quadratic: ((text{endX}^3/3 + text{endX}^2 + text{endX} – (text{startX}^3/3 + text{startX}^2 + text{startX})))
  • Cubic: ((text{endX}^4/4 + text{endX}^2/2 – (text{startX}^4/4 + text{startX}^2/2)))
  • Exponential: (e^{text{endX}} – e^{text{startX}})

The result fields are formatted to display numbers up to two or three decimal places, depending on context, ensuring precision in the output values.

Final Note:

Make sure to correctly input all the required values respecting the validation rules to ensure accurate calculations. With these steps, you should be able to effectively use the Function Table Calculator for generating detailed tables of function values and their derivatives and integrals.