Young Geniuses · Ages 13 to 14

Transformation of Functions Match

Match each function transformation to its effect on the graph. A Grade 8–9 functions worksheet with answer keys.

Match WorksheetGrades functions, transformations, matching5 difficulty levels8 questions

The learning journey

Every activity is one step. Here is where this one fits.

  1. PlayLearn the idea in a game
  2. Practise(you are here)Lock it in on paper
  3. ReviewCome back and keep it sharp
  4. MasterTake on a harder challenge
  5. AchieveEarn a certificate

About Transformation of Functions Match

Transformation of Functions Match helps upper-secondary learners understand how changing a function changes its graph. Down one side are transformations written in function notation — adding a constant outside the function, adding inside the function, multiplying by a constant, and negating the function — and down the other their effect on the graph, such as shifting up, shifting left, stretching vertically or reflecting in the x-axis; the student joins each to the right description. Graph transformations are a core Grade 8 to 9 and early high-school topic across the US, UK, Canada and Australia, and they reveal the deep connection between algebra and geometry: a small change to a formula produces a predictable movement of its graph. The notation can be slippery — changes inside the bracket affect the input and behave in ways that often surprise students — so a matching task that pairs notation with effect is exactly the right practice for building secure understanding. The four core transformations give clean, unambiguous matching. The five levels reshuffle the layout so the activity stays fresh. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving the correct effect for each transformation. There is no advertising and no sign-up.

Common questions

What transformations are covered?
Shifts, stretches and reflections written as f(x)+a, f(x+a), a·f(x) and −f(x).
What grade is this for?
Grade 8 to Grade 9 learners aged 13 to 14.
Is an answer key included?
Yes, every level gives the correct effect for each transformation.

A hand for grown-ups

Before you start
Find a calm few minutes with no rush. Let your child know it is fine to find some of it tricky — that is what practice is for.
While they work
Sit nearby but let them lead. If they get stuck, ask "what could you try?" rather than giving the answer — the thinking is the point.
Afterwards
Ask them to show you one they found easy and one they found hard. Praise the effort on the hard one, not just the right answers.
Watch out for
Rushing. If answers come too fast and wrong, slow the pace down together rather than pushing for more.
Away from the screen
Look for the same maths in everyday life — counting stairs, sharing snacks, spotting shapes on a walk.

Chosen by the skills this activity practises.