Graph y=7^x

Problem

y=7

Solution

1. Identify the type of function. This is an exponential function of the form y=bx where the base b=7 Since b>1 the graph represents exponential growth.

2. Determine the y-intercept. Set x=0 to find the point where the graph crosses the y-axis.

y=7=1

The y-intercept is (0,1)

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

y=7=7

For x=−1

y=7(−1)=1/7≈0.14

4. Identify the horizontal asymptote. As x approaches negative infinity, 7 approaches 0

Horizontal Asymptote: *y=0

5. Sketch the graph. Draw a smooth curve that passes through (−1,1/7) (0,1) and (1,7) staying above the x-axis and increasing rapidly as x increases.

Final Answer

y=7

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