Logarithmic and Exponential Functions: Graphs
Activity
Since all exponential functions pass the horizontal line test, they are one-to-one functions. As a result, each exponential function has an inverse. These inverse functions are known as logarithmic functions.
if and only if
The graph of and the graph of are given in the applet.
Explore the Sliders:
Use the sliders to adjust the base of the exponential and logarithmic functions.
Observe how changing the base affects the shape of both graphs.
Input Your Values:
In the input boxes, type different values for the exponent or logarithmic arguments. Observe how the graphs update based on your inputs.
Compare the Functions:
Identify how the graphs of the exponential function and its logarithmic inverse reflect over the line . Check if each point on the exponential function has a corresponding inverse point on the logarithmic function.
Analyze Symmetry:
Experiment with different values to see the symmetry between exponential and logarithmic graphs.
Try to predict the graph of the logarithmic function based on changes you make to the exponential function.
Q1
Find the inverse of the function
Q2
Find the domain and range of and
Q3
Verify the domain and range from the graph