Graphing Calculator Online
Plot up to four functions on one coordinate plane. Change the viewing window, trace values, zoom, pan and build a table without installing software or sending your equations to a calculation server.
Last Updated: July 26, 2026Online Function Graph Calculator
Enter each expression as the right side of y = f(x). The default window runs from -10 to 10 on both axes. Use radians for standard trigonometric graphs.
Viewing window
Move across the graph to trace x and the plotted function values.
Ready. Two example functions are plotted.
Function Value Table
Create up to 101 rows for every enabled function.
| x | y1 = x^2 - 4 | y2 = 2*x + 1 |
|---|---|---|
| -2 | 0 | -3 |
| -1 | -3 | -1 |
| 0 | -4 | 1 |
| 1 | -3 | 3 |
| 2 | 0 | 5 |
How to Use This Graphing Calculator
- Enter a function in one of the equation fields. Type the expression after
y =, such asx^2 - 4,sin(x)or1/x. - Keep the checkbox selected for every function you want to compare. You can draw four curves at the same time.
- Set the minimum and maximum values for the x-axis and y-axis. Start with -10 to 10 when you do not know the best window.
- Choose radians or degrees before plotting a trigonometric function. Standard algebra and precalculus graphs normally use radians.
- Select Plot Functions. Move over the graph to trace values. Drag the plot to pan, or use the zoom controls to inspect a smaller or larger region.
- Enter a start value, end value and positive step under Function Value Table. Select Build Table to compare exact sampled outputs.
The plot updates from the expressions and window you choose. A blank, disabled or invalid function does not stop other valid functions from drawing. The page identifies syntax errors beside the affected equation so you can correct the input without losing the rest of the graph.
What This Function Graph Calculator Does
A graphing calculator turns numerical function values into points on a Cartesian coordinate plane. For each sampled input x, the calculator evaluates the expression to obtain y. It then maps the ordered pair (x, y) to a pixel inside the selected viewing window. Closely spaced valid points form the visible curve.
This tool plots explicit real-valued functions written as y = f(x). It supports polynomial, rational, exponential, logarithmic, root, absolute-value and trigonometric expressions. It does not solve implicit relations such as x^2 + y^2 = 25, polar equations, inequalities, three-dimensional surfaces or piecewise syntax. Use the dedicated Equation Calculator when you need an algebraic solution instead of a visual function plot.
Supported notation and functions
| Input | Meaning | Example | Domain note |
|---|---|---|---|
+ - * / ^ | Arithmetic and powers | 3*x^2 - 2*x + 1 | Division requires a nonzero denominator. |
sin cos tan | Trigonometric functions | sin(x) | Uses the selected RAD or DEG mode. |
asin acos atan | Inverse trigonometric functions | asin(x) | asin and acos require -1 ≤ x ≤ 1. |
sqrt abs | Square root and absolute value | sqrt(x + 3) | Real square roots require an input of at least zero. |
ln log exp | Natural log, base-10 log and ex | ln(x) | Log inputs must be positive. |
floor ceil round sign | Step and sign functions | floor(x) | Jumps appear as separate plotted segments. |
pi e | Mathematical constants | sin(2*pi*x) | 2pi also works through implicit multiplication. |
You may write y = or f(x) = before an expression. Multiplication can be explicit, as in 2*x, or implicit in common forms such as 2x, 3(x + 1) and 2sin(x). Function arguments need parentheses. Enter sin(x), not sin x.
Graphing Formula and Coordinate Mapping
For a function y = f(x), every permitted x input produces one output. The calculator samples inputs from the left edge of the viewing window to the right edge. It converts mathematical coordinates to canvas positions using the window bounds and graph dimensions.
pixelX = (x - xMin) / (xMax - xMin) × graphWidth
pixelY = graphHeight - (y - yMin) / (yMax - yMin) × graphHeight
The subtraction in the pixelY formula reverses the browser canvas direction. Mathematical y-values increase upward, while canvas pixel positions increase downward. Grid intervals use rounded 1, 2 or 5 multiples of powers of ten so labels remain readable as you zoom.
Worked Example: Graph y = x² - 4
Enter x^2 - 4 in the first function field. This quadratic is a parabola that opens upward. Its axis of symmetry is x = 0 because no linear x term is present.
| x | Calculation | y | Point |
|---|---|---|---|
| -2 | (-2)² - 4 | 0 | (-2, 0) |
| -1 | (-1)² - 4 | -3 | (-1, -3) |
| 0 | 0² - 4 | -4 | (0, -4) |
| 1 | 1² - 4 | -3 | (1, -3) |
| 2 | 2² - 4 | 0 | (2, 0) |
The vertex is (0, -4), and the x-intercepts are (-2, 0) and (2, 0). The y-intercept is also the vertex because x = 0 gives y = -4. Plot 2*x + 1 in a second field to compare the parabola with a line. Their visible crossing points estimate the solutions to x^2 - 4 = 2x + 1. Use an equation solver when exact roots are required.
Choose the Right Viewing Window
The viewing window controls which part of a graph you see. A correct function may look blank when every output falls above or below the selected y-range. It may look almost flat when the window is too wide. Start with a balanced window, then zoom around the feature you need.
- Use x from -10 to 10 and y from -10 to 10 for many introductory algebra functions.
- Use x from about -6.5 to 6.5 and y from -2 to 2 for two periods of
sin(x)orcos(x)in radians. - Use a positive x-range for
ln(x)andlog(x), because logarithms are undefined at zero and for negative real inputs. - Use a narrow y-range around zero to inspect intercepts, but do not mistake a visual crossing for an exact symbolic solution.
- Select Reset View to restore -10 to 10 without changing the equations.
Common Function Graphs
| Function type | Example | Typical shape | Important feature |
|---|---|---|---|
| Linear | 2*x + 1 | Straight line | Slope is 2 and y-intercept is 1. |
| Quadratic | x^2 - 4 | Parabola | Vertex and symmetry help locate minimum or maximum values. |
| Absolute value | abs(x - 2) | V shape | The corner occurs where the expression inside abs equals zero. |
| Rational | 1/x | Two branches | x = 0 is outside the domain and acts as a vertical asymptote. |
| Exponential | exp(x) | Rapid growth | The graph stays positive and passes through (0, 1). |
| Logarithmic | ln(x) | Slow growth | The domain is x > 0, and the graph passes through (1, 0). |
| Trigonometric | sin(x) | Repeating wave | In radians, the period is 2π and the range is [-1, 1]. |
Domain, Range and Discontinuities
The domain is the set of x-values for which a function is defined. The range is the set of outputs it produces. A plot samples only the selected window, so it shows a visible portion of the domain and range rather than proving their complete mathematical limits.
Undefined samples create gaps. For 1/x, the denominator becomes zero at x = 0, so the calculator does not connect the two branches across that point. For sqrt(x), negative inputs are skipped. For ln(x), zero and negative inputs are skipped. Vertical asymptotes and steep changes are separated when adjacent samples jump too far across the graph.
Function Transformations
Graphing a base function with a transformed version helps you see shifts, reflections and stretches. If the base function is y = f(x), common transformations follow these patterns:
Horizontal shift: y = f(x - h)
Vertical scale or reflection: y = a·f(x)
Horizontal scale: y = f(bx)
For example, compare x^2 with (x - 3)^2 + 2. The second parabola moves three units right and two units up. Compare sin(x) with 2*sin(x) to see a vertical stretch from amplitude 1 to amplitude 2. Enter both versions in separate rows so the change stays visible.
Graphing Calculator vs Other Math Tools
Choose a tool by the result you need. A graph helps you inspect shape and behavior, while a solver or calculator may provide a more exact numerical or symbolic answer.
| Tool | Best use | Main output |
|---|---|---|
| Graphing Calculator | Comparing functions, windows, curves and visual intersections | Coordinate plot, trace values and table |
| Scientific Calculator | Evaluating one numerical expression with trig, logs, roots and powers | Numerical result |
| Algebra Calculator | Simplifying, evaluating or solving supported algebra tasks | Algebra result and steps |
| Equation Calculator | Solving one-variable linear or quadratic equations | Exact and decimal solutions |
| Quadratic Equation Calculator | Analyzing ax² + bx + c = 0 from coefficients | Roots, discriminant, vertex and checks |
| System of Equations Calculator | Solving simultaneous 2×2 or 3×3 linear systems | Exact system solution and row operations |
Accuracy, Privacy and Method
The calculator uses browser-based IEEE 754 number arithmetic. This provides about 15 to 17 significant decimal digits for many values, but some decimal fractions and transcendental results cannot be represented exactly. The displayed graph is also limited by screen resolution, sampling density and the selected window.
The expression engine reads a defined list of numbers, operators, functions, constants and parentheses. It does not execute the entered text as JavaScript. Expressions longer than 180 characters, unsupported names, unmatched parentheses, excessive nesting and non-finite results receive controlled errors. Your expressions and table settings stay in the current page. Reloading clears them.
The function definitions, domain concepts and transformation patterns follow the open educational references in OpenStax Precalculus 2e: Functions and Function Notation and Transformation of Functions. Verify repeatable issues through the 1Dollars contact page with the expression, angle mode and viewing window used.
Related Calculators
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Frequently Asked Questions
What expressions can this graphing calculator plot?
It plots explicit real-valued functions of x using arithmetic, powers, parentheses, constants and supported trig, root, logarithmic, exponential, rounding and absolute-value functions.
Can I graph more than one equation?
Yes. Enter and enable up to four functions. Each curve uses a separate color, and the trace readout lists the output of every valid plotted function at the pointer’s x-value.
Should I use degrees or radians?
Use the unit required by your problem. Standard function graphs usually use radians. Choose degrees when x-values represent degree measures, such as sin(30) = 0.5.
How do I type x squared?
Enter x^2. The caret means “raised to the power.” For a shifted square, use parentheses, such as (x - 3)^2.
Why is part of my graph missing?
The function may be outside the viewing window or undefined for those x-values. Adjust the window and check domain limits such as x > 0 for logarithms.
Does the graph show exact intercepts?
The trace gives numerical estimates based on sampled points and screen coordinates. Use algebra or a dedicated equation calculator when an exact intercept or root is required.
How do I graph a vertical line?
This tool accepts y as a function of x, so one x input must produce one y output. A vertical line such as x = 3 is not supported in the current explicit-function plotter.
Can I make a table of values?
Yes. Set the start x, end x and positive step. The tool creates up to 101 rows for each enabled valid function and marks undefined outputs clearly.
Are my equations stored?
No calculation server receives the expressions. Plotting and tables run in the current browser page. Reloading the page clears the entered functions and settings.
Why can a graph differ from a textbook image?
Different axis windows, aspect ratios, angle modes, sampling and rounding can change the picture. Match the textbook window and confirm that the expression uses the same parentheses and units.
Financial and educational disclaimer: This calculator provides general mathematical estimates for learning and checking work. It is not financial, engineering, scientific, tax or professional advice. Verify important equations, units, domains, precision requirements and results before making a decision.