Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Identify the y-intercept of an exponential function
Problem
For \(f(x)~=~7\cdot~2^{x}\), verify the \(y\)-intercept by substitution, then state the horizontal asymptote and range.
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What this problem is really about
The y-intercept comes from the zero input, and exponentials make that evaluation especially revealing. We’ll use the zero-exponent rule to separate the initial coefficient from the growth factor, then write the intercept as an ordered pair. Finally, we’ll use the absence of a vertical shift and the positivity of the factors to identify the approached level and allowable outputs.
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