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))

Complete and Continue