Graph 3^x

Problem

y=3

Solution

1. Identify the type of function, which is an exponential growth function because the base b=3 is greater than 1

2. Determine the y-intercept by substituting x=0 into the equation, giving y=3=1

3. Find additional points to plot by substituting integer values for x

x=−1⇒y=3(−1)=1/3

x=1⇒y=3=3

x=2⇒y=3=9

4. Identify the horizontal asymptote, which is the line y=0 (the x-axis), as 3 approaches 0 when x becomes more negative.

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

Final Answer

y=3

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