which is the graph of $f(x)=3(\\frac{2}{3})^x$?
which is the graph of $f(x)=3(\\frac{2}{3})^x$?
Answer
Explanation:
Step1: Analyze the general form of exponential - function
The general form of an exponential function is (y = ab^{x}), where (a) is the initial value ((y) - intercept when (x = 0)) and (b) is the base. For the function (f(x)=3(\frac{2}{3})^{x}), when (x = 0), (f(0)=3(\frac{2}{3})^{0}=3\times1 = 3). So the (y) - intercept is at the point ((0,3)).
Step2: Analyze the behavior of the function based on the base
Since the base (b=\frac{2}{3}) and (0\lt b\lt1), the function is a decreasing exponential function. As (x\to+\infty), (y = f(x)\to0), and as (x\to-\infty), (y = f(x)\to+\infty).
Answer:
The graph with a (y) - intercept at ((0,3)) and is a decreasing exponential function approaching the (x) - axis as (x) increases. (Based on the given options, you would select the graph that has (y = 3) when (x = 0) and is decreasing).