graph the function.\ng(x)=2cdot3^{x}
graph the function.\ng(x)=2cdot3^{x}
Answer
Explanation:
Step1: Find the y - intercept
Set (x = 0). Then (g(0)=2\times3^{0}=2\times1 = 2). So the y - intercept is the point ((0,2)).
Step2: Find another point
Set (x = 2). Then (g(2)=2\times3^{2}=2\times9 = 18). So we have the point ((2,18)).
Step3: Analyze the behavior
As (x\to-\infty), (3^{x}\to0), so (g(x)=2\times3^{x}\to0). The function (y = g(x)) is an exponential growth function since the base (a = 3>1) and the coefficient of (3^{x}) is positive ((2>0)).
Answer:
The graph of (y = 2\times3^{x}) has a y - intercept at ((0,2)), passes through the point ((2,18)), approaches the x - axis as (x\to-\infty) and increases rapidly as (x) increases.