EXPONENTIAL FUNCTIONS: GRAPHS GROWTH AND DECAY

An exponential function is a number raised to a variable exponent. Exponential terms are generated by repeated multiplication by a growth or decay factors. Exponential functions and their inverses, logarithmic functions are known as a transcendental functions. 
An exponential function with base b is given by \(f\left( x \right) = a{b^x}\). The x in the expression is the exponent, this is the independent variable.

Example 1:
For the given function f(x)=3^x
a) Determine if is a growth or decay function.
b) Sketch the graph of the function using an input and output table.
c) State the domain, and range, intercepts, zeros, and intercepts, asymptotes.

Solutions:
a) The exponential functions f(x)=3^x is a growth functions since b the base  is equal to 3 which is greater than 1. (b = 3 > 1⇒ f(x) is a growth function) 

b) Graph

c: 
Domain        Interval: (-∞,∞)  or ℝ
                     Inequality: -∞ < x < ∞
Range           Interval: (0,∞)  
                     Inequality: x > 0
Intercepts      y-intercept y = 0
                      x-intercept or zeros none
Asymptotes  Horizontal Asymptote: y =0
                     Vertical Asymptote: note

Exponential and Logarithmic Functions Playlist