4.5 Exploring Properties of Exponential Functions.notebook 2015 05 11 May 11, 2015 4.5 Exploring Properties of Exponential Functions Exponential functions are functions that can be written in the form f(x) = a(b)x, where "b" is the base of the exponential function and "a" is the initial value of the function (which is the point at which the curve crosses the y‐axis). Functions of the form f(x) = a(b)x have the following properties; 1. When b > 1, the graph will show exponential growth, which means that it will increase as you move from left to right. eg. y=2x 2. When 0 < b < 1, the graph will show exponential decay, which means x that it will decrease as you move from left to right. eg y=(1/3) 3. The graph will have a horizontal asymptote along the x‐axis. 4. The graph has a domain of { x∈R } and a range of { y>0,y∈R } exponential decay exponential growth a a asymptote 1 4.5 Exploring Properties of Exponential Functions.notebook May 11, 2015 First and Second Differences In previous math classes you would have seen that the y‐values of linear functions increase by the same amount for every increase by one in the x‐values (i.e. the same first differences). Last year we learned to identify quadratic functions by their second differences, that is the differences in the first differences. Exponential functions do not have a common first or second difference, but they do share a common first ratio, that is the y‐ values are related by a multiplicative factor. 2 4.5 Exploring Properties of Exponential Functions.notebook May 11, 2015 3 4.5 Exploring Properties of Exponential Functions.notebook May 11, 2015 Ex. Identify whether the following tables of values represent linear, quadratic or exponential functions. Pg. 216 #1b,c,does this graph display growth or decay? Pg. 243 #1,2 4