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Have you ever noticed how sound decreases in intensity as we move away from its source? Or how the pH of a solution changes? These phenomena can be modeled with logarithmic function graphs. Let's learn the characteristics and how to draw logarithmic function graphs.
Logarithmic function graphs have a distinctive shape different from other functions. Let's look at the basic graph for various base values.
For function with :
Let's learn the steps to draw logarithmic function graphs with concrete examples.
Drawing
To draw this graph, we create a table of values by choosing values that are powers of :
Drawing
For base , the graph will be decreasing:
Let's compare logarithmic graphs with different bases on one coordinate system:
| Property | ||
|---|---|---|
| Graph direction | Increasing (monotonic) | Decreasing (monotonic) |
| Domain | ||
| Range | All real numbers | All real numbers |
| -intercept | ||
| Vertical asymptote |
Logarithmic graphs can be transformed in various ways:
We can shift the logarithmic function graph by adding or subtracting a constant to the function.
We can shift the logarithmic function graph by adding or subtracting a constant to the function.
Create a value table and draw the graphs of:
Determine the domain, range, and asymptote of function .
If and , determine:
Sketch the graph of and determine the -intercept.
Value tables:
For :
For :
For :
For :
For :
