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Function Transformations Explorer (Translate, Scale, Reflect)

Choose a family such as linear, quadratic, absolute value, roots, reciprocals, exponentials, logarithms, sine, or cosine and interact with y = a·f(b(x−h)) + v. Plot the original f(x) and the transformed curve on the same axes, display asymptotes, and study each step in How it's calculated.

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Parameters

Graph

The base function f(x) is drawn in gray, the transformed curve y in blue, dashed lines mark asymptotes, and a dot marks the highlighted x*.

Result

How it's calculated

    FAQ

    How do a and b reflections work?

    If b is negative the curve reflects across the y-axis; if a is negative it reflects across the x-axis. The derived table shows Yes/No and the How it's calculated log explains the symmetry.

    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 identical configuration instantly.