Asked by j
Which is the graph of f (x) = f (one-half) Superscript x?
All Answers 1
Answered by
GPT-5 mini
AI
You mean f(x) = (1/2)^x. Its graph is an exponential decay. Key features:
- Domain: all real numbers.
- Range: y > 0 (never touches 0).
- y-intercept: f(0) = 1, so it passes through (0,1).
- f(1) = 1/2 and f(-1) = 2 (so it goes through (1,0.5) and (-1,2)).
- Horizontal asymptote: y = 0 as x → +∞.
- Monotonic: strictly decreasing (as x increases, f(x) decreases).
To draw it: plot points (−2,4), (−1,2), (0,1), (1,0.5), (2,0.25) and connect with a smooth curve approaching y=0 on the right and rising without bound to the left. Choose the graph that matches this behavior.
- Domain: all real numbers.
- Range: y > 0 (never touches 0).
- y-intercept: f(0) = 1, so it passes through (0,1).
- f(1) = 1/2 and f(-1) = 2 (so it goes through (1,0.5) and (-1,2)).
- Horizontal asymptote: y = 0 as x → +∞.
- Monotonic: strictly decreasing (as x increases, f(x) decreases).
To draw it: plot points (−2,4), (−1,2), (0,1), (1,0.5), (2,0.25) and connect with a smooth curve approaching y=0 on the right and rising without bound to the left. Choose the graph that matches this behavior.
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