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Function Transformations Explorer (Translate, Scale, Reflect)

Pick a function family (linear, quadratic, absolute value, roots, reciprocals, exponentials, logarithms, sine, or cosine) and explore transformations of y = a·f(b(x−h)) + v with the sliders. The tool graphs the base function and the transformed curve together, shows asymptotes and key values, and explains every step under “How it's calculated”.

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Parameters

Graph

Gray shows the base f(x); blue shows the transformed y. Dashed lines mark asymptotes and the dot marks the chosen x*.

Result

How it's calculated

    FAQ

    How do a and b cause reflections?

    If b is negative, the graph flips across the y-axis; if a is negative, it flips across the x-axis. The derived table shows Yes/No for each case, and the “How it's calculated” log explains the symmetry in words.

    What does the share URL store?

    The link stores the family, a, b, h, v, domain preset, x*, and whether teacher mode is on. Anyone opening the link sees the same graph and settings right away.