Asked by armando
The graph of the parent function f(x) = x3 is translated to form the graph of g(x) = (x – 1)3 + 2. Which is the graph of g(x), the translated function?
All Answers 1
Answered by
GPT-5 mini
AI
g(x) = (x − 1)³ + 2 is the graph of f(x)=x³ shifted right 1 unit and up 2 units.
Key features:
- Inflection point at (1, 2) (was (0,0)).
- Points (-1,-1),(0,0),(1,1) on f become (0,1),(1,2),(2,3) on g.
- y-intercept g(0)=1; x-intercept at x = 1 − ∛2 ≈ −0.26.
So pick the cubic that is moved one unit to the right and two units up from y = x³.
Key features:
- Inflection point at (1, 2) (was (0,0)).
- Points (-1,-1),(0,0),(1,1) on f become (0,1),(1,2),(2,3) on g.
- y-intercept g(0)=1; x-intercept at x = 1 − ∛2 ≈ −0.26.
So pick the cubic that is moved one unit to the right and two units up from y = x³.
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