Graph Inverse Functions
Example 1: Graph the inverse of \(y=2 \cdot3^x\).
Example 1: Graph the inverse of \(y=2 \cdot3^x\).
To graph logarithmic functions of the form \(f\left(x\right)=a\log_b\left(x-h\right)+k\):
1. Graph the parent function\(f\left(x\right)=\log_b\left(x\right)\) (you may find it helpful to convert this to its equivalent exponent form and
create a table of values where you pick the y-value and solve for the x-value).
2. Follow the order of operations as you transform the function, similar to graphing exponential functions.
3. Complete the horizontal translation. Remember, this will also shift the vertical asymptote \(h\) units left or right.
4. Multiply each \(y\) coordinate by \(a\) to either vertically stretch or compress the graph.
5. Complete the vertical translation indicated by the \(k\) value.
Example 2: Graph the function \(f\left(x\right)=2\log_2\left(x+1\right)-3\). Include the graph of the parent function, describe the transformations and find the domain and range of the translated function.
Don’t confuse graphing the inverse with graphing the function! It is a common mistake.
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