Graph F(x)=3^x

Problem

F(x)=3

Solution

1. Identify the type of function. This is an exponential function of the form y=ax where the base a=3 Since 3>1 the graph represents exponential growth.

2. Determine the horizontal asymptote. As x approaches negative infinity, 3 approaches 0 Therefore, the horizontal asymptote is the line y=0

3. Calculate the y-intercept. Set x=0 to find F(0)=3=1 The point is (0,1)

4. Evaluate additional points to determine the shape.
   For x=1 F(1)=3=3 The point is (1,3)
   For x=2 F(2)=3=9 The point is (2,9)
   For x=−1 F*(−1)=3(−1)=1/3 The point is (−1,1/3)

5. Sketch the curve. Draw a smooth curve passing through the points (−1,1/3) (0,1) (1,3) and (2,9) ensuring the curve stays above the x-axis and rises rapidly to the right.

Final Answer

F(x)=3

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