Graph f(x)=5^x

Problem

ƒ(x)=5

Solution

1. Identify the type of function. This is an exponential function of the form ƒ(x)=bx where the base b=5 Since b>1 the function represents exponential growth.

2. Determine the horizontal asymptote. As x approaches negative infinity, 5 approaches 0 Therefore, the horizontal asymptote is the line y=0

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

ƒ(0)=5=1

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

ƒ(1)=5=5

ƒ*(−1)=5(−1)=1/5=0.2

ƒ(2)=5=25

5. Sketch the graph by plotting the points (−1,0.2) (0,1) and (1,5) then drawing a smooth curve that increases rapidly to the right and approaches the x-axis to the left.

Final Answer

ƒ(x)=5

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