Year 9 Maths • AC9M9A06 • Authored homework
Function transformations
Describe and sketch transformations of familiar functions, including translations, reflections and simple dilations. Connect equations, tables and graphs to explain what changes and what stays the same. Show working, use correct units or notation, and check reasonableness.
Part A
Short-answer questions
For y = x^2 + 3, describe the transformation from y = x^2.
For y = (x - 4)^2, describe the transformation from y = x^2.
State the reflection that changes y = f(x) into y = -f(x).
If y = f(x) is shifted 2 units left, write the transformed function using f notation.
Describe how y = 2x^2 differs from y = x^2.
Find the new vertex of y = (x + 1)^2 - 5.
Explain the difference between a vertical translation and a horizontal translation.
Sketch the effect of changing y = x^2 to y = -x^2.
Correct this error: y = (x + 3)^2 moves y = x^2 three units right.
Give one real-world graph where shifting or scaling a function could be useful.
Part B
Long-answer questions
Compare y = x^2, y = x^2 + 4 and y = (x - 3)^2 using words, a table and graph features.
Describe and sketch the transformation from y = x^2 to y = -2(x + 1)^2 + 3.
Given key points on y = f(x), find the matching points after the transformation y = f(x) - 5.
Explain why horizontal transformations inside brackets can feel opposite to the sign shown.
Use a graph to compare a vertical dilation and a vertical translation of y = x^2.
Create two different transformations of y = |x| and describe their vertices and shape.
A parabola has vertex (4, -2) and opens upward with the same width as y = x^2. Write a possible equation.
Model a real situation by shifting a basic function, then explain what each transformation represents.
Identify and correct three transformation mistakes in a student sketch of y = -(x - 2)^2 + 1.
Write a full explanation linking function notation, graph movement and transformed coordinates.
Part C
Research and understanding task
Choose a simple base graph such as y = x, y = x^2 or y = |x|. Create three transformations, sketch or describe each graph, and explain a real-world meaning for at least one transformation.