Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Graph an exponential growth function
Problem
Graph \(f(x)~=~3\cdot~2^{x}\) on the grid. State the initial value, growth factor and percent, verified points and ratio, horizontal asymptote, domain, and range.
An exponential graph is built from a starting output and a repeated multiplicative factor. We’ll evaluate the zero input for the initial value, convert the factor into a percent change, and generate points by multiplying for equal input steps. Constant output ratios verify the pattern, while positivity and the absence of a vertical shift determine the asymptote, domain, and range.
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