Advanced MathVery hardTransforming a function's graph
Advanced Math practice question
The function f is defined by f(x) = x². The graph of g in the xy-plane is the graph of f shifted 4 units to the right and 1 unit up. Which equation defines g?
- A. g(x) = (x − 4)² + 1Correct
- B. g(x) = (x + 4)² + 1
- C. g(x) = (x − 4)² − 1
- D. g(x) = (x + 1)² − 4
Answer: A. g(x) = (x − 4)² + 1
Right 4 replaces x with x − 4; up 1 adds 1.
Why the other answers are wrong
- B. g(x) = (x + 4)² + 1
- x + 4 shifts left.
- C. g(x) = (x − 4)² − 1
- −1 shifts down.
- D. g(x) = (x + 1)² − 4
- This shifts left 1 and down 4.
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