Calculated Result
Graph
Computed Data Table
| # | x | f(x) | g(x) | h(x) = f(x) - g(x) |
|---|
Calculator
Expression tips: use x, sin(x), cos(x), tan(x), log(x), sqrt(x), exp(x), and ^ for powers.
Formula Used
Main rule: h(x) = f(x) - g(x)
This calculator subtracts one function from another point by point. At every chosen x value, it computes f(x), computes g(x), then subtracts to get h(x).
Point evaluation: h(a) = f(a) - g(a)
Table generation: the calculator repeats that subtraction for all x values from the selected start to end range using the chosen step size.
Simplification: the calculator also simplifies the algebraic form of f(x) - g(x) when possible, giving a cleaner difference expression.
How to Use This Calculator
- Enter the first expression in the f(x) field.
- Enter the second expression in the g(x) field.
- Choose a single x value if you need one direct evaluation.
- Set the range start, range end, and step size.
- Choose decimal places and maximum rows if needed.
- Press Subtract Functions to generate results.
- Review the simplified expression, evaluated values, graph, and data table.
- Download the current results as CSV or PDF if required.
Example Data Table
This example uses f(x) = x2 + 1 and g(x) = |x|, so h(x) = x2 + 1 - |x|.
| x | f(x) | g(x) | h(x) |
|---|---|---|---|
| -2 | 7 | 2 | 5 |
| -1 | 2 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 4 | 1 | 3 |
| 2 | 11 | 2 | 9 |
About This Function Difference Tool
A function subtraction calculator helps you compare two expressions over one point or across an entire interval. It is useful in algebra, precalculus, calculus preparation, graph comparison, model comparison, and classroom practice.
Instead of subtracting isolated numbers, you subtract outputs that come from two separate rules. This creates a new function that can be simplified, evaluated, graphed, and exported for later review. Seeing all three curves together often makes relationships easier to understand.
Use this page when you need quick checks, homework support, table generation, graph inspection, or printable summaries for notes and assignments.
FAQs
What does function minus a function mean?
It means subtracting one function from another at the same input value. If h(x) = f(x) - g(x), then each output of g(x) is subtracted from the corresponding output of f(x).
Can I enter polynomials, trigonometric terms, and logarithms?
Yes. You can enter expressions such as x^2+3*x-1, sin(x), cos(x), exp(x), log(x), sqrt(x), and combinations of them, provided the expression is valid.
Why do some rows show invalid values?
Some expressions are undefined for certain x values. Examples include log(x) when x is zero or negative, or division by zero. Those points are skipped in graphs and marked invalid in tables.
What is the simplified difference expression?
It is the algebraic result of combining f(x) and g(x) into one expression. For example, if f(x)=x^2+2 and g(x)=x, then h(x)=x^2-x+2.
Can I plot all three functions together?
Yes. The graph displays f(x), g(x), and the difference h(x) across the selected range, helping you compare shapes, crossings, and output gaps visually.
What range settings should I use?
Choose a start, end, and step that fit your problem. Smaller steps give smoother curves and more rows. Larger steps reduce the number of calculated points.
What does the evaluation point do?
The evaluation point calculates f(x), g(x), and h(x) for one chosen x value. It is useful when homework asks for the exact difference at a specific input.
Can I download the results?
Yes. Use the CSV option for spreadsheet work and the PDF option for printable summaries. Both export the current computed data table and key result details.