Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Identify the horizontal asymptote of an exponential function
Problem
Identify the horizontal asymptote of the exponential function \(f(x)=3(2)^x\).
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What this problem is really about
For a transformed exponential, the horizontal asymptote comes from the outside vertical shift, not the coefficient or base. We’ll rewrite the rule in coefficient-base-shift form, distinguish a vertical stretch from a vertical translation, and test far-left values. Their approach identifies the horizontal level the graph gets arbitrarily close to without ever attaining.
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