Graphing Calculator

Plot functions of x, compare curves on the same axes, and explore how each equation behaves.

Functions

Use x, pi, e, powers, and functions such as sin(x) or sqrt(x).

y =

Try an example

x minx maxy miny max

Drag the graph to pan. Use the controls to zoom or reset the viewing window. Curves are calculated in your browser.

Sample value table

Function	x = -2	x = -1	x = 0	x = 1	x = 2
x^2 - 4	0	-3	-4	-3	0

A graph turns a formula into a shape

For an explicit function y = f(x), every allowed x-value is paired with an output. Plotting many of those pairs reveals intercepts, turning points, symmetry, periodic behavior, growth, and discontinuities that may be harder to notice in the formula alone.

This tool plots up to four functions of x on the same coordinate plane. You can hide a curve, drag to pan, zoom, set exact axis limits, and trace coordinates. The explanation button sends the visible functions to the shared tutor for a step-by-step analysis.

How to use the graphing calculator

Enter one or more functions

Use one row for each function of x. Add, hide, or remove curves when you want to compare their shapes.

Set a useful viewing window

Pan, zoom, or enter axis limits so roots, turning points, and asymptotes are not hidden outside the frame.

Ask about the visible features

Send the visible functions to the tutor for help with intercepts, domain, range, transformations, or asymptotes.

Points on a function graph

Choose an input x, calculate f(x), and plot the ordered pair. Repeating that process across the domain traces the curve.

y = f (x) ⟺ (x, f (x))

A reliable way to work through it

Enter one explicit function per row

Use x as the variable. Add more rows when you want to compare equations on the same axes.

Choose a useful viewing window

A curve can look empty or misleading when its important features lie outside the current x or y range.

Confirm features algebraically

Use the graph to locate likely roots or turning points, then solve or differentiate when an exact value matters.

Worked example

Analyze the graph of y = x² - 4

y = x^{2} - 4 = (x - 2) (x + 2)

Factoring shows x-intercepts at x = -2 and x = 2.

x = 0 ⟹ y = - 4

The y-intercept is (0, -4), which is also the vertex.

x^{2} \geq 0 ⟹ x^{2} - 4 \geq - 4

The parabola opens upward, so its minimum output is -4.

The graph has vertex (0, -4), x-intercepts (-2, 0) and (2, 0), y-intercept (0, -4), domain all real numbers, and range y ≥ -4.

Common mistakes to check

Trusting the default window

A root, asymptote, or turning point may exist outside the visible range. Adjust the axes before concluding it is absent.

Connecting across a discontinuity

Functions such as 1/x have separate branches. A vertical asymptote is not part of the graph.

Reading an estimate as exact

A traced coordinate is a numerical estimate unless algebra or another exact method confirms it.

Slope CalculatorFind rise over run from two points or read the slope from a line equation.Domain and Range CalculatorFind valid inputs and possible outputs from a function formula, with restrictions written in interval or set-builder notation.Derivative CalculatorDifferentiate a function, identify each rule, and simplify the result one step at a time.Function Composition CalculatorSubstitute one function into another in the correct order, simplify it, and determine where the composition is defined.

Questions students ask

How many functions can I graph at once?

You can plot up to four explicit functions of x and hide individual curves while comparing them.

Which function syntax is supported?

Use arithmetic, parentheses, powers with ^, x, pi, e, and common functions such as sin, cos, tan, sqrt, abs, ln, log, and exp.

Can this graph implicit or polar equations?

Not yet. The current tool focuses on explicit functions in the form y = f(x).

Why is my graph not visible?

Check the expression for an error, then reset or widen the viewing window. The function may also be undefined over the visible x-range.