About the Graphing Calculator
This online graphing calculator plots functions of x in your browser — polynomials, trigonometric, exponential, logarithmic, absolute value and root functions. Type y = f(x), optionally add a second function g(x) to compare, set the x-range, and the graph redraws instantly.
Beyond the picture it does the analysis students usually do by hand: it finds the x-intercepts (roots), the points where the two graphs intersect, the y-intercept, the value at any x you choose, and the lowest and highest values on the visible range. A table of values lists points you can copy into homework or a spreadsheet.
It is built for algebra, pre-calculus and calculus students checking their work, teachers projecting examples, and anyone who wants to see how changing a coefficient changes a curve. Angles are in radians. Roots are found numerically: crossings are located by bisection and points where the graph only touches the axis (like x² at 0) by a local minimum search, so results are accurate to about 6 significant figures.
How to use the graphing calculator
- 1Type the first function after f(x) =, e.g. x^2 - 4 or sin(x).
- 2Optionally add a second function g(x) to compare or find intersections.
- 3Set the x-range to zoom in or out.
- 4Enter an x value to read f(x) and g(x) at that point.
- 5Read the roots, intersections and y-intercept, and use the table of values.
Formula and method
The graph is drawn by evaluating the function at evenly spaced x values across your range and joining the points. Points where the function is undefined (for example √x for negative x, or 1/x at 0) are left out so the curve breaks instead of showing a false line.
Roots are found by scanning 800 small steps for a change of sign and narrowing each one down by bisection; places where the curve touches the axis without crossing are found by refining local minima of |f(x)|. Sign changes caused by a vertical asymptote (such as 1/x at 0) are rejected. Intersections are the roots of f(x) − g(x). Minimum and maximum values are taken from 400 samples across the range, so very narrow spikes may be slightly underestimated.
- f(x), g(x)
- The functions being plotted
- x-range
- The interval of x shown on the graph and searched for roots
Worked examples
Parabola x² − 4 and line 2x + 1
x² − 4 = 0 at x = ±2. Setting x² − 4 = 2x + 1 gives x² − 2x − 5 = 0, so x = 1 ± √6 ≈ −1.449 and 3.449. At x = 3, f = 5 and g = 7.
Sine wave from −2π to 2π
sin(x) crosses zero at −2π, −π, 0, π and 2π, which are all inside the range. Its peak value is 1, reached at x = π/2 ≈ 1.5708.
Cubic x³ − 3x
x³ − 3x = x(x² − 3) has roots at 0 and ±√3 ≈ ±1.732. At x = 2 the value is 8 − 6 = 2.
Touching root: (x − 1)² on [−2, 4]
The parabola (x − 1)² touches the x-axis at x = 1 without crossing it — a double root. Its lowest value is 0 there and its highest on the range is (−2 − 1)² = 9; at x = 3 it equals 4.
Frequently asked questions
How do I graph a function online?+
Type the function in terms of x, such as 2x + 3 or x^2 − 5x + 6, and set the x-range. The graph updates immediately, and you can add a second function to compare two curves.
How do I find where two graphs intersect?+
Enter both functions as f(x) and g(x). The calculator solves f(x) = g(x) numerically across the range and lists every x where the curves cross; substitute into either function to get the y value.
How do I type powers, roots and trig functions?+
Use ^ for powers (x^3), sqrt(x) for square roots, cbrt(x) for cube roots (x^(1/3) is only defined for x ≥ 0), and sin(x), cos(x), tan(x) with x in radians. Use ln(x) for natural log, log10(x) for base 10, abs(x) for absolute value, and pi and e as constants.
Why does my graph have gaps?+
Gaps appear where the function is undefined or extremely large — for example √x for negative x, ln(x) for x ≤ 0, or tan(x) near π/2. Leaving them out avoids drawing misleading vertical lines.
What is the y-intercept of a graph?+
The y-intercept is where the graph crosses the y-axis, found by evaluating f(0). For y = 2x + 1 it is 1, and for y = x² − 4 it is −4.