Graph f(x)=2^x

Problem

ƒ(x)=2

Solution

1. Identify the function type as an exponential function with a base b=2 which is greater than 1 indicating exponential growth.

2. Determine the horizontal asymptote, which for the parent function ƒ(x)=bx is the line y=0

3. Calculate key points by substituting integer values for x

• If x=−1 ƒ*(−1)=2(−1)=1/2

• If x=0 ƒ(0)=2=1

• If x=1 ƒ(1)=2=2

• If x=2 ƒ(2)=2=4

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

5. Sketch a smooth curve passing through these points, approaching the x-axis as x→−∞ and increasing rapidly as x→∞

Final Answer

To graph ƒ(x)=2 plot the points (−1,0.5) (0,1) (1,2) and (2,4) and draw a curve that approaches the horizontal asymptote y=0

Want more problems? Check here!