Q:

Consider the exponential function f(x) = 3(1/3)^x and its graphWhich statements are true for this function and graph? Check all that apply.The initial value of the function is 1/3.The growth value of the function is 1/3.The function shows exponential decay.The function is a stretch of the function f(x) = (1/3)^xThe function is a shrink of the function f(x) = 3^xOne point on the graph is (3, 0).

Accepted Solution

A:
An exponential function is of the form f(x)=a[tex]b^{x}[/tex]where a ≠0, b > 0 , b ≠1, and x is any real number.when b > 1, the graph increases. when 0 < b < 1, the graph decreases. a = initial value,r = growth or decay ratex = number of time.The given Exponential function is [tex]f(x)=3(\frac{1}{3})^x[/tex]Among the options given the ones which are true for the given function are:The growth value of the function is 1/3 The function shows exponential decay The function is a stretch of the function f(x)  =[tex](\frac{1}{3})^x[/tex]