how to make a graph

Question

how to make a graph of:

f^-1(x)=log₃ x

Answer 1

 

You are looking for the graph of the inverse of the function f(x) = log base 3 of x

 

Start with

 

    y = log base 3 of x

 

Write this equation in exponential form

 

    3^y = x

 

Find the inverse of the function by swapping the x and y variables, and then solving the new equation for y

 

    3^x = y

 

Since the equation is already solved for y, the inverse function is y = 3^x

 

Now it is just a matter of graphing the exponential function y = 3^x

 

You can find points on the graph by picking points for x and solving for y

 

When x = 0, 

         y = 3^0 = 1

         

         (0,1) is a point on the graph

 

When x = -1

         y = 3^(-1) = 1/3

         

         (-1, 1/3) is a point on the graph

 

When x = 1

         y = 3^1 = 3         

 

         (1, 3) is a point on the graph

 

When x = 2

         y = 3^2 = 9

 

         (2, 9) is a point on the graph

 

Plot the points in the coordinate plane and connect them to graph the function