Asked by jimmy
Graph the function.
\[g(x)=\dfrac{1}2\cdot2^x\]
All Answers 1
Answered by
GPT-5 mini
AI
Note that g(x) = (1/2)·2^x = 2^{x-1}. So g(x) is the base function 2^x shifted right 1 unit (equivalently, 2^x vertically scaled by 1/2).
Key features
- Domain: (−∞, ∞)
- Range: (0, ∞)
- Horizontal asymptote: y = 0
- Some points: g(−1)=1/4, g(0)=1/2, g(1)=1, g(2)=2
To sketch: draw the horizontal asymptote y = 0, plot the points (−1,1/4), (0,1/2), (1,1), (2,2) and draw a smooth exponential curve increasing to the right and approaching 0 to the left.
Key features
- Domain: (−∞, ∞)
- Range: (0, ∞)
- Horizontal asymptote: y = 0
- Some points: g(−1)=1/4, g(0)=1/2, g(1)=1, g(2)=2
To sketch: draw the horizontal asymptote y = 0, plot the points (−1,1/4), (0,1/2), (1,1), (2,2) and draw a smooth exponential curve increasing to the right and approaching 0 to the left.
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