Translations, Reflections and Stretches

Translations, Reflections and Stretches

A transformation changes a parent graph in predictable ways. In $y=a f(x+p)+q$, the outside $q$ moves the graph up or down, the inside $p$ moves it in the opposite horizontal direction, and $a$ stretches or reflects vertically. State the transformation from the parent, then identify invariant features such as asymptotes where relevant.

Worked reasoning

From $y=x^2$ to $y=2(x-3)^2+1$: move right 3, stretch vertically by 2, then move up 1. The turning point moves from $(0,0)$ to $(3,1)$.

Exam method

1. Name the parent function. 2. Read inside changes before outside changes. 3. Transform key points/features and check with a sketch.

Features survive transformation

Rather than plotting many random points, transform a few important features: intercepts, vertex, asymptotes or a simple parent point. Record each move in the order it occurs. For instance, a reflection outside the function changes y-values, whereas a reflection inside changes x-values. When an IEB-style question asks for the effect of a parameter, explain it in words and support it with one transformed coordinate. This shows why the feature moves as claimed.

One-minute retrieval: Translations, Reflections and Stretches

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.