Graph y=4^x

Problem

y=4

Solution

1. Identify the type of function. This is an exponential function of the form y=bx where the base b=4 Since b>1 the graph represents exponential growth.

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

y=4=1

The y-intercept is at (0,1)

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

y=4=4

For x=−1

y=4(−1)=1/4=0.25

For x=2

y=4=16

4. Identify the horizontal asymptote. As x approaches negative infinity, 4 approaches 0 Therefore, the horizontal asymptote is the line y=0 (the x-axis).

5. Sketch the curve. Plot the points (−1,0.25) (0,1) and (1,4) Draw a smooth curve that rises sharply to the right and flattens toward the x-axis to the left.

Final Answer

y=4

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