Transformation — Algebra I · Grade 9 or accelerated Grade 8, what it means and where it is taught
A change to the function that moves or stretches its graph.
Taught in Algebra I · Grade 9 or accelerated Grade 8.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Function — A rule pairing each input with exactly one output.
Practise this idea
4 questions in the course bank use Transformation, in Translations, Reflections & Rotations, Congruence & Sequences of Transformations, Writing & Transforming Linear Functions.
Problem 1
Point (5, -2) maps to (-5, -2). Which single transformation was used?
Worked answer
reflection across the y-axis
The x changed sign; the y did not
That is the rule (x, y) → (-x, y)
A reflection across the y-axis
Problem 2
Triangle ABC has A(1, 2), B(5, 2), C(1, 6). Its image is A'(2, -1), B'(2, -5), C'(6, -1). Which transformation was used?
Worked answer
rotation of 90 degrees clockwise about the origin
A(1,2) → (2, -1) ✓
B(5,2) → (2, -5) ✓
C(1,6) → (6, -1) ✓
That rule is a 90° clockwise rotation, also called 270° counter-clockwise
Problem 3
Which single transformation has the same effect as reflecting across the x-axis and then across the y-axis?
Worked answer
a 180 degree rotation about the origin
(3, 5) → (3, -5) → (-3, -5)
Both coordinates ended up negated
That is the rule for a 180° rotation about the origin
Problem 4
Describe the transformation from f(x) = x2 to g(x) = (x - 2)2 + 5.
Worked answer
right 2 and up 5
(x - 2) shifts right 2
+5 shifts up 5