Function Asymptotes Visualizer

Find vertical, horizontal, and oblique asymptotes of common functions and watch them drawn as color-coded dashed lines over the curve. One-sided limit probes report whether each vertical asymptote tends to plus or minus infinity from each side, and four transformation sliders let you watch every asymptote track shifts and scales in real time.

Function Composition Visualizer

Pick an outer function f and an inner function g from ten base families to see both compositions plotted on the same graph — f composed with g in blue, g composed with f in amber. The visual contrast makes it immediate that composition is not commutative, while live symbolic expressions and special-case notes for identity and inverse pairs build the intuition behind f of g of x.

The Domain Card and Applied Chips

Inverse Function Visualizer

Plot any function alongside its inverse as a reflection across the line y = x. Pick a base function — linear, cubic, reciprocal, exponential, logarithmic, square root, quadratic, absolute, sine, or cosine — apply affine transformations, and watch the inverse re-derived symbolically in real time. For functions that need a domain restriction to be invertible, the discarded portion appears faded and the principal branch in bold.

Piecewise Function Builder

Build piecewise functions piece by piece — pick a shape from a catalog, set each piece

Range of a Function Visualizer

See the set of achievable outputs of any function drawn directly on the y-axis as a colored band, with a horizontal number line below the plot and a draggable test point that checks whether any specific y-value is reached. Pick from eleven base functions grouped by range shape and watch the range respond live to vertical scale and shift — while horizontal transformations leave it unchanged.

Function Reflections Visualizer

Pick a base function — linear, quadratic, cubic, reciprocal, exponential, logarithmic, sine, cosine, absolute value, or square root — and switch between seven reflection types: across the x-axis, y-axis, y = x, the horizontal y = c, the vertical x = c, plus |f(x)| and f(|x|). Both curves draw together, with the axis of reflection highlighted in orange.

Function Symmetry Visualizer

See whether any function is even, odd, or neither by plotting f(x) alongside its y-axis reflection f(-x) and its origin rotation -f(-x) on one graph. Overlapping curves prove the symmetry visually, a color-coded verdict card states the result, and a step-by-step algebraic derivation walks through the test. Transformation sliders let you watch shifts break even or odd symmetry in real time.

Tangent Line Visualizer

Drag the x₀ slider and watch the tangent line follow the curve in real time. Pick a base function — linear, quadratic, cubic, reciprocal, exponential, logarithmic, square root, absolute, sine, cosine — apply affine transformations, and read both the point-slope and slope-intercept forms of the tangent equation alongside the slope m = f

The Four Tabs and the Custom Tab

Functions Families Gallery

Pick a function family from a sidebar of twelve standard families — linear, quadratic, cubic, power, rational, exponential, logarithmic, sine, cosine, tangent, absolute value, and square root — and adjust its parameters with live sliders. The plot, symbolic equation, and explanation panel update in real time, with the three trigonometric families grouped together for direct comparison.