Properties of Exponential Functions
Exponents Review
- positive exponents are just repeated multiplication
- e.g. 5^3 = 5*5*5 = 125
- 2^6 = 2*2*2*2*2*2 = 64
- negative exponents are the reciprocal of the positive exponent
- e.g. 3^(-3) = 1/(3^3) = 1/27
- 4^(-2) = 1/(4^2) = 1/16
Introduction to Exponential Functions
- exponential functions have "x" as an exponent, like y = 3^x or y = 0.8^x
Characteristics of Exponential Function
- y = c^x, where c is any number greater than zero (0.1, 0.6, 2, 5, etc)
- if c > 1, the function is increasing, meaning as x increases, y increases
- if 0 < c < 1, the function is decreasing, meaning as x increases, y decreases
Graphing an Exponential Function Using a Graphing Calculator
- when inputting an exponential function into your graphing calculator, put the entire exponent in brackets
- e.g. y = 4^(x - 2)
- y = 2^(3(x + 1))