Transformations of graphs of functions

Topics

Function graphs and solution sets

One function graph can be reshaped by a transformation, and its place relative to the x-axis reads off solutions of equations and inequalities.

Works

Work

Inverse function by reflection

Functions and analysis High-school concept

Drag a point on the graph and watch (a, b) reflect across y = x to (b, a) on the inverse.

Work

Function graph transformations

Functions and analysis High-school concept

Drag a, b, h, and k to see how y = a f(b(x - h)) + k shifts, stretches, and flips a basic graph.

Exam visualizations

Exam

A parabola under a restricted translation

115 GSAT Mathematics A, Fill-in 16 Vertex form of a quadraticTranslation of a graph

115 GSAT Mathematics A, Fill-in 16: keep the vertex on one line and the graph through one fixed point, then discard the translation that leaves the parabola where it was.

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