Graph 2^x

Problem

y=2^x

Solution

1. Identify the type of function. This is an exponential function of the form y=b^x where the base b=2 is greater than 1 indicating exponential growth.

2. Determine the horizontal asymptote. As x approaches negative infinity, 2^x approaches 0 Therefore, the horizontal asymptote is the line y=0

3. Calculate key points to plot. Choose several values for x and solve for y

• If x=−1 y=2^(−1)=0.5

• If x=0 y=2^0=1

• If x=1 y=2^1=2

• If x=2 y=2^2=4

• If x=3 y=2^3=8

4. Plot the points (−1,0.5) (0,1) (1,2) (2,4) and (3,8) on a coordinate plane.

5. Sketch a smooth curve passing through these points, ensuring the curve stays above the x-axis and rises more steeply as x increases.

Final Answer

To graph y=2^x plot the points (−1,0.5) (0,1) (1,2) and (2,4) then draw a curve that approaches y=0 as x⇒−∞

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