Graph y=3^x

Problem

y=3

Solution

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

2. Determine the y-intercept by substituting x=0

y=3

y=1

The y-intercept is at the point (0,1)

3. Calculate additional points to define the shape of the curve.
   For x=1

y=3=3

For x=2

y=3=9

For x=−1

y=3(−1)=1/3

4. Identify the horizontal asymptote. As x approaches negative infinity, 3 approaches 0

Horizontal Asymptote:y=0

5. Sketch the curve. Start near the x-axis on the left side, pass through (0,1) (1,3) and (2,9) and rise steeply to the right.

Final Answer

y=3

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