Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Match an exponential equation to graph features
Problem
Analyze \(y=4\cdot~2^{x}\).
Big Picture
What this problem is really about
Matching an exponential rule to a graph requires every major feature to agree. We’ll evaluate the zero input for the vertical intercept, combine the base and coefficient signs to determine direction, and locate any outside vertical shift for the asymptote. Those same parameters determine whether the graph approaches from above or below and which output values belong to its range.
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