Skill: function-transformations

Function Transformations Practice

An endless supply of never-repeating transformation problems with instant feedback. Describe shifts, spot reflections and stretches, and track vertices through y = a(x − h)² + k — the one template that transforms any function.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Right triangles

How to enter answers

Directions: type up, down, left, or right.
Shifts with distance: type right 5 or left 2 (direction, then units).
Vertices: type the point as 3,2 or (3, 2).
Yes / no: just type yes or no. Numbers: 3 or a fraction like 1/2.

2 What you’ll practice

Every problem is generated fresh from 12 templates — a problem never repeats until its whole pool is used up.

Shifts

h moves left/right, k moves up/down. Inside the function → opposite direction; outside → as written.

y = x² + 3 → shift up 3

Stretch, compress & reflect

|a| > 1 stretches, 0 < |a| < 1 compresses, negative a flips over the x-axis.

y = −x² → reflect over x-axis

Vertex tracking

Only h and k move the vertex. Track (0, 0) inside-out through each transformation.

y = (x−3)²+2 → vertex (3, 2)

3 Watch out for these

The three mistakes students make most often on Pythagoras problems.

1. Reading (x + 4) as “right 4”

Wrong: y = (x + 4)² shifts right 4. Right: shift left 4 — inside changes go opposite. Ask what x zeroes the inside.

2. Scrambling the order

Wrong: shifting up before reflecting, then misplacing the vertex. Right: work inside-out: (x − h) first, then a, then k.

3. Calling 2x² a “shift up 2”

Wrong: y = 2x² moves the parabola up 2. Right: multiplication reshapes (stretch); addition relocates (shift). The vertex stays at (0, 0).

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