General Form and Graph for an Exponential Function

A function whose input (x) is located in the exponent. Example: Jason has $17 and quadruples his money every month. Write an equation to represent the situation. Exponential Equation Initial Multiplier

Exponential Table There is a constant MULTIPLIER between consecutive output values. XY x3

For any Exponential: Graphs of y=b x 0 < b < 1 b = 1 b > 1 Increasing, asymptote y=0 Decreasing, asymptote y=0 Horizontal line y=1 Domain: x-intercept(s): y-intercept(s): Vertical asymptote: None (0,1) b > 0 Range:

Representations of y=ab x xy=a(b)xy=a(b)x The initial value The multiplier a (0,a) Context: a is the starting point b is the multiplier x b

Why b>0 in y=b x xy=(-2) x UGLY GRAPH!