Graph y=3(2)^x

Problem

y=3*(2)x

Solution

1. Identify the type of function. This is an exponential growth function of the form y=a*(b)x where a=3 and b=2

2. Determine the y-intercept. Set x=0 to find y=3*(2)0 which simplifies to y=3*(1)=3 The point is (0,3)

3. Calculate additional points to define the curve. For x=1 y=3*(2)1=6 For x=2 y=3*(2)2=12 For x=−1 y=3*(2)(−1)=1.5

4. Identify the horizontal asymptote. As x approaches negative infinity, y approaches 0 The horizontal asymptote is the line y=0

5. Plot the points (−1,1.5) (0,3) (1,6) and (2,12) on a coordinate plane and draw a smooth curve that increases from left to right, staying above the x-axis.

Final Answer

y=3*(2)x

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