Calxsolver
Graphing

Function Grapher

Enter a function of x and an interval. The calculator samples the function, plots it as a smooth curve, locates the zeros by bisection and the local extrema from sign changes of the derivative, then overlays every feature on the plot.

Function Grapher

Plot y = f(x) with zeros, extrema and the y-intercept marked.

Try:
Answer2 zeros, 1 extremum on [-5, 5]
-5-4-3-2-1012345-505101520(-2, 0)(2, 0)min (0.025, -3.99937)y-int (0, -4)xf(x)
  1. Functionf(x) = x^2 - 4
  2. Rangex ∈ [-5, 5]
  3. Zerosx = -2, x = 2
  4. y-intercept(0, -4)
  5. Local extremamin at x = 0.025 (y = -3.99937)
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Worked examples

Graph y = x² − 4 Plot a parabola and read off its zeros, vertex and y-intercept.

Frequently asked questions

What syntax does f(x) accept?

Standard arithmetic and the usual functions: sin, cos, tan, exp, ln, log, sqrt, abs and ^ for powers. Constants pi and e are built in.

Are the zeros exact?

They are numerical, found by sign changes between samples and refined with bisection to many significant figures — well below the plot resolution.

Can it handle vertical asymptotes?

Yes. When the function value jumps by an outlier amount between two adjacent samples (as for 1/(x − 1)), the polyline is broken so the asymptote is not drawn as a vertical line.

Related solvers

Multi-Function Grapher Plot two functions on one chart and locate every intersection. Parametric Grapher Plot a parametric curve (x(t), y(t)) over an interval in t. Polar Grapher Plot a polar curve r = f(θ) — roses, cardioids, spirals, conics. Inequality Region Grapher Shade the region y > f(x), y < f(x), y ≥ f(x) or y ≤ f(x). Function Feature Analyser Zeros, extrema, monotonicity, asymptotes and end behavior — without a plot. Function Value Table Tabulate f(x) at evenly spaced x values — useful for sketching by hand.