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- Transformations of graphs
Transformations of graphs
Changing an equation slightly moves, stretches or reflects its graph in a predictable way.
Translations
y = f(x) + a moves the graph up by a.
y = f(x + a) moves the graph left by a (the opposite of what you might expect).
y = f(x − 3) moves it right by 3.
y = f(x + a) moves the graph left by a (the opposite of what you might expect).
y = f(x − 3) moves it right by 3.
Reflections
y = −f(x) reflects in the x-axis.
y = f(−x) reflects in the y-axis.
y = f(−x) reflects in the y-axis.
Using turning points
If y = f(x) has a turning point at (2, 5):
y = f(x) + 3 → (2, 8)
y = f(x + 1) → (1, 5)
y = −f(x) → (2, −5)
y = f(x) + 3 → (2, 8)
y = f(x + 1) → (1, 5)
y = −f(x) → (2, −5)
y = x2 has a turning point at (0, 0). Where is the turning point of y = (x − 4)2 + 1?
- (x − 4): move right 4
- + 1: move up 1
Answer: (4, 1)
f(x) + a moves up a; f(x + a) moves left a; −f(x) reflects in the x-axis; f(−x) reflects in the y-axis.
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