Graph f(x)=3^x

Problem

ƒ(x)=3

Solution

1. Identify the type of function, which is an exponential function with a base b=3

2. Determine the horizontal asymptote, which for the basic form bx is the line y=0

3. Calculate the y-intercept by evaluating ƒ(0)

ƒ(0)=3=1

4. Find additional points to determine the shape of the curve.

ƒ(1)=3=3

ƒ(2)=3=9

ƒ*(−1)=3(−1)=1/3

5. Plot the points (−1,1/3) (0,1) (1,3) and (2,9) on a coordinate plane.

6. Sketch a smooth curve that increases rapidly to the right and approaches the x-axis as x decreases to the left.

Final Answer

The graph of ƒ(x)=3 is an increasing exponential curve passing through (0,1) and (1,3) with a horizontal asymptote at y=0

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