Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Sketch an exponential graph from a table
Problem
Use the table to determine the multiplicative pattern and initial value, write the exponential equation, and state its behavior, horizontal asymptote, domain, and range.
A table with equally spaced inputs is exponential when consecutive outputs share a constant ratio. We’ll test those ratios, use the zero-input row as the initial coefficient, and reconstruct a rule that reproduces every row. The factor then determines growth and percent change, while the rule’s sign and vertical shift determine the curve’s asymptote, domain, and range.
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