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Graphing Logarithmic Functions

Graphing Logarithmic Functions 1.2 - Solution

arrow_back Return to Graphing Logarithmic Functions
a
To draw the graph of a logarithmic function, we can follow a three-step process.
  1. Identify the base.
  2. Determine points on the graph.
  3. Plot the points and sketch the graph.

Let's do it!

Identifying the Base

Looking at the given functions, we can see that we have a common logarithm and natural logarithm. Recall that the base of the common logarithm is and the natural logarithm has the number as its base. With this in mind, let's highlight the base of each function.

Determining Points on the Graph

Using the base we can identify three points on the graph of a logarithmic function. Since we know the bases, we can immediately determine these points.

Function Points
and
and
and

Plotting the Points and Sketch the Graph

Finally, we will plot the points and connect them with a smooth curve.

b
To find the listed attributes of the logarithmic functions and we will use their graphs we made in Part A.

We can see that, for the three functions, the variable takes values greater than and the values are all real numbers. Therefore, the three functions have the same domain and range. We can also see that, for the three functions, their values approach infinity as approaches infinity, and their values approach negative infinity as approaches on the positive side. The line is the vertical asymptote of the three graphs. None of them have a horizontal asymptote. The intercept is the same for the three graphs, and it occurs at None of the graphs intercept the axis, as it is a vertical asymtpote. The three graphs increase in their entire domain, and are negative for values of greater than and less than Lastly, the three graphs are positive for values greater than