Graph y=3(2)^x

Problem

y equals 3 times 2 to the x-th power

Solution

1. Identify the type of function. This is an exponential growth function of the form y equals a times b to the x-th power where a equals 3 and b equals 2

2. Determine the y-intercept. Set x equals 0 to find y equals 3 times 2 to the 0 power which simplifies to y equals 3 times 1 equals 3 The point is open paren 0 comma 3 close paren

3. Calculate additional points to define the curve. For x equals 1 y equals 3 times 2 to the first power equals 6 For x equals 2 y equals 3 times 2 squared equals 12 For x equals negative 1 y equals 3 times 2 to the negative 1 power equals 1.5

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

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

Final Answer

y equals 3 times 2 to the x-th power

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