Function Plotter Controls
Plot up to six expressions. Use x as the variable. Separate functions with semicolons or new lines.
Formula Used
The plotter samples x values across the selected interval. It evaluates each function and maps the resulting y values onto the canvas.
How to Use This Calculator
- Enter one function per line, or separate expressions with semicolons.
- Set the horizontal range and choose automatic or manual vertical limits.
- Adjust samples, grid spacing, line width, and analysis options.
- Press Plot Functions. The result appears above the form.
- Move the cursor across the graph, then export the plot or data.
Function Plotting Guide
Understanding Function Plots
A function plot turns an equation into a visible curve. Each horizontal position represents an x value. The calculator evaluates the expression at that point. The resulting y value sets the vertical position. Repeating this process across the selected range creates the complete graph. Axes, labels, and grid lines make patterns easier to understand.
Choosing the Right Expression
Enter expressions using x as the variable. Standard operators include addition, subtraction, multiplication, division, and powers. Common functions include sine, cosine, tangent, logarithms, square roots, and absolute values. Multiplication signs must be written clearly. For example, enter 2*x instead of 2x. Parentheses help control calculation order and prevent ambiguous results.
Setting Graph Ranges
The x range controls which horizontal values appear. The y range controls the visible height. Narrow ranges reveal local details. Wider ranges show behavior. Automatic y scaling estimates useful limits from valid sample points. Manual limits are better when comparing several graphs. Avoid equal minimum and maximum values because a visible interval is required.
Sampling and Accuracy
A plotted curve is built from many calculated points. More samples create smoother lines. They also require more browser work. Discontinuous functions need handling. The calculator avoids connecting points when values become invalid or jump sharply. This reduces misleading vertical lines near asymptotes. Very high sampling may not improve a simple straight line.
Reading Important Features
Roots occur where the curve crosses the horizontal axis. Turning points appear where the graph changes direction. Intercepts show where the curve meets either axis. A derivative curve displays estimated slope values. Positive derivative values indicate rising sections. Negative values indicate falling sections. Values near zero can signal flat points, peaks, or valleys.
Comparing Multiple Functions
Several formulas can be plotted together. Separate each expression with a semicolon or a new line. The legend identifies every curve. You can inspect growth rates, intersections, shifts, and symmetry. Use related equations to study transformations. For example, compare x^2, (x-2)^2, and x^2+3.
Formula Used
For every sample, the calculator selects x between the chosen limits. It evaluates y=f(x). Screen coordinates use proportional mapping. The horizontal position is (x-xmin)/(xmax-xmin) times the canvas width. The vertical position reverses direction because screen pixels increase downward. Numerical derivatives use the central difference formula, [f(x+h)-f(x-h)]/(2h), with a small step h.
How to Use This Calculator
Enter one or more valid functions. Choose horizontal limits first. Select automatic or manual vertical scaling. Set the sample count and grid spacing. Enable any desired analysis options. Press the plot button. The result appears above the form. Review the legend, coordinate readout, roots, and derivative information. Adjust ranges when important details remain hidden.
Practical Plotting Tips
Start with moderate limits and about one thousand samples. Add parentheses around grouped terms. Use pi and e for common constants. Zoom by reducing the x or y interval. Increase samples for rapid oscillations. Disable point markers when curves become crowded. Compare one change at a time. This makes transformations easier to recognize and explain.
Frequently Asked Questions
1. Which function syntax is supported?
Use x, numbers, parentheses, commas, standard operators, and named functions. Supported names include sin, cos, tan, asin, acos, atan, sqrt, abs, exp, ln, log, floor, ceil, round, min, max, pow, sec, csc, and cot.
2. Can I plot several functions together?
Yes. Enter each function on a new line or separate formulas with semicolons. The calculator supports up to six expressions and displays a matching legend.
3. How do I enter powers?
Use the caret symbol. For example, x^2 plots a parabola. Parentheses are recommended for grouped powers such as (x-2)^3.
4. Are trigonometric inputs measured in radians?
Yes. Trigonometric functions use radians. Enter pi for π. For example, sin(pi/2) evaluates to one.
5. How does automatic vertical scaling work?
Automatic scaling reviews finite sampled values and reduces the influence of extreme outliers. It then adds padding so the main curves remain visible.
6. Why are some lines intentionally broken?
Functions with asymptotes can jump between very large values. Breaking those segments prevents a false vertical line from appearing across the graph.
7. How are roots estimated?
The calculator detects sign changes between neighboring samples. It then applies repeated interval narrowing to estimate each crossing within the selected tolerance.
8. Is the derivative exact?
No. The derivative uses a central numerical difference. Smaller step values can improve local accuracy, but extremely small values may introduce floating-point noise.
9. Why does my function produce no visible curve?
The expression may be undefined across the selected range, outside manual y limits, or written with unsupported implicit multiplication. Try 2*x instead of 2x.
10. Can I export my results?
Yes. Download the visible plot as a PNG image or export sampled coordinates as a CSV file for further analysis.
11. Does the graph work on mobile screens?
Yes. The canvas resizes to available width. Inputs also change from three columns to two columns, then one column on mobile devices.