Graph f(x)=4^x

Problem

ƒ(x)=4

Solution

1. Identify the type of function, which is an exponential function with a base b=4 Since b>1 the graph represents exponential growth.

2. Determine the horizontal asymptote. As x approaches negative infinity, 4 approaches 0 so the horizontal asymptote is the line y=0

3. Calculate the y-intercept by evaluating the function at x=0

ƒ(0)=4=1

The y-intercept is (0,1)

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

ƒ(1)=4=4

ƒ*(−1)=4(−1)=1/4=0.25

ƒ(2)=4=16

5. Sketch the graph by plotting the points (−1,0.25) (0,1) and (1,4) then drawing a smooth curve that rises from left to right, staying above the x-axis.

Final Answer

ƒ(x)=4

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