Graph exponential, logarithmic, and trigonometric functions with key features.
Analyze exponential factor, reflection, and graph behavior
Problem
Analyze \(f(x)~=~8(0.5)^x\). State \(a,~b,~h,~\text{and}~k\); classify growth or decay and any reflection; give the intercepts, asymptote, domain, range, and monotonic behavior; and compute exact anchors at \(x~=~-1,~0,~\text{and}~1\).
Separate the exponential base from the outside coefficient before describing the graph. A base between zero and one determines decay, while the coefficient’s sign determines reflection and which side of the horizontal asymptote contains the range. Exact inputs one unit apart then reveal the repeated factor and provide a clean check on the monotonic direction.
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