Advanced MathMediumTranslating an exponential graph
Advanced Math practice question
The graph of y = 2ˣ in the xy-plane is translated 3 units to the right and 1 unit down. Which of the following is an equation of the resulting graph?
- A. y = 2^(x − 3) − 1Correct
- B. y = 2^(x + 3) − 1
- C. y = 2^(x − 3) + 1
- D. y = 2ˣ − 4
Answer: A. y = 2^(x − 3) − 1
A shift right by 3 replaces x with x − 3; a shift down by 1 subtracts 1: y = 2^(x − 3) − 1.
Why the other answers are wrong
- B. y = 2^(x + 3) − 1
- x + 3 shifts the graph left.
- C. y = 2^(x − 3) + 1
- +1 shifts the graph up.
- D. y = 2ˣ − 4
- Subtracting 4 only moves the graph down; there is no horizontal shift.
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