Graph f(x)=3^x

Problem

f with hook of x equals 3 to the x-th power

Solution

1. Identify the type of function, which is an exponential function with a base b equals 3

2. Determine the horizontal asymptote, which for the basic form b to the x-th power is the line y equals 0

3. Calculate the y-intercept by evaluating f with hook of 0

f with hook of 0 equals 3 to the 0 power equals 1

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

f with hook of 1 equals 3 to the first power equals 3

f with hook of 2 equals 3 squared equals 9

f with hook times negative 1 equals 3 to the negative 1 power equals one third

5. Plot the points open paren negative 1 comma one third close paren open paren 0 comma 1 close paren open paren 1 comma 3 close paren and open paren 2 comma 9 close paren on a coordinate plane.

6. Sketch a smooth curve that increases rapidly to the right and approaches the x-axis as x decreases to the left.

Final Answer

The graph of f with hook of x equals 3 to the x-th power is an increasing exponential curve passing through open paren 0 comma 1 close paren and open paren 1 comma 3 close paren with a horizontal asymptote at y equals 0

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