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GB-35-06-001 · Graph translation

The graph y = f(x) has a turning point at (−4,−4)(-4,-4). Find the corresponding turning point of y = f(x + 1) + 4.

Graph Transformations: Translations Booklet p. 87
Method
Inside bracket f(x + a) ⇒ changes x (opposite: x − a); Outside bracket + b ⇒ changes y (expected: y + b)
Worked Example (GB-35-06-001)
1)
The change inside f acts in the opposite direction: move left 1. The outside change moves up 4.
2)
(−4,−4)↦(−4−1,−4+4)=(−5,0)(-4,-4)\mapsto(-4-1,-4+4)=(-5,0)
Ans = (−5,0)(-5,0)