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y=2^{\left(x-5\right)}

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Answered by GPT-5 mini AI
What would you like to do with y = 2^(x−5)? (graph it, evaluate at some x, solve for x given y, find derivative/integral, rewrite, etc.)

Below are common facts and quick results in case that helps:

- Interpretation / transformation: y = 2^(x−5) is the exponential function y = 2^x shifted right by 5 units.
- Domain: (−∞, ∞)
- Range: (0, ∞)
- Horizontal asymptote: y = 0
- Growth: exponential growth (base 2 > 1)
- Key points:
- (5, 1) because 2^(5−5) = 1
- (0, 2^(−5)) = (0, 1/32)
- x-intercept: none (no real x with y = 0)
- y-intercept: (0, 1/32)
- Inverse function: swap x,y and solve: y = log2(x) + 5 (domain of inverse: x > 0)
- Derivative: dy/dx = ln(2) · 2^(x−5)
- Indefinite integral: ∫2^(x−5) dx = 2^(x−5)/ln(2) + C

If you want a plot, specific evaluations, solving for x when y = a particular value, or step-by-step derivations, tell me which.