Graph y=2^x

Problem

y=2

Solution

1. Identify the type of function, which is an exponential function with a base of 2

2. Determine the horizontal asymptote, which is the line y=0 because 2 approaches 0 as x approaches negative infinity.

3. Calculate the y-intercept by substituting x=0 into the equation.

y=2=1

4. Find additional points to determine the shape of the curve.

x=−1⇒y=2(−1)=0.5

x=1⇒y=2=2

x=2⇒y=2=4

x=3⇒y=2=8

5. Plot the points (−1,0.5) (0,1) (1,2) (2,4) and (3,8) on a coordinate plane and draw a smooth curve that increases from left to right, staying above the x-axis.

Final Answer

The graph of y=2 is an increasing exponential curve passing through (0,1) and (1,2) with a horizontal asymptote at y=0

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