Functions & Graphs

8 interactive Mathematics simulations on functions & graphs.

Mathematics · Functions & Graphs Rational functions – asymptotes of the graph For y = (ax + b)/(cx + d) or y = (ax² + bx + c)/(x + d), drag the coefficients to see the vertical, horizontal and oblique asymptotes... Ages 17–18
Mathematics · Functions & Graphs Limits of Sequences and Functions, Continuity Sequence mode: the points (n, uₙ) approach the line y = L; a draggable band L ± ε shows that from some index N₀ onward every term stays... Ages 16–17
Mathematics · Functions & Graphs Exponential function y = aˣ and logarithmic function y = logₐx The graphs of y = aˣ and y = logₐx are reflections of each other across the line y = x. Drag point M on the exponential graph and its... Ages 16–17
Mathematics · Functions & Graphs Linear functions – graphs and the equation ax + b = 0 Graph of y = ax + b on the coordinate plane. Drag the point on the y-axis to change b, drag the second point to change the slope a, and... Ages 13–14
Mathematics · Functions & Graphs Continuity of a function at a point A piecewise function joined at x₀, with an adjustable parameter m. The simulation computes the left-hand limit, the right-hand limit and... Ages 16–17
Mathematics · Functions & Graphs Cubic and rational function analysis – derivatives, extrema, asymptotes Plots y = ax³ + bx² + cx + d or y = (ax + b)/(cx + d) alongside a variation table built live from the sign of y'. Drag point M along the... Ages 17–18
Mathematics · Functions & Graphs Quadratic function y = ax² + bx + c: vertex, axis of symmetry, variation table The parabola y = ax² + bx + c is graphed with three sliders for a, b, c right in the simulation; students can also drag the vertex I... Ages 15–16
Mathematics · Functions & Graphs Parabola y = ax² and quadratic equations The graph of y = ax² together with the line y = bx + c. Drag the point on the parabola to change a (opens up/down, narrow/wide), and... Ages 14–15