Discuss the curve under the guidelines of Section 3.5.
To discuss: The curve using the guidelines.
Given curve is .
Let the curve be .
The logarithmic function is defined only for all positive values of x.
Here, that is for all . Therefore, the function is defined only when
Therefore, the domain of the curve is .
To obtain the y-intercepts, substitute in .
The y-intercept for the function is
To obtain the x-intercepts, substitute in and solve for x.
The x-intercept of the function is .
If for all x in D, then f is an even function and the curve is symmetric about the y-axis.
If for all x in D, then f is an odd function and the curve is symmetric about the origin.
If for all x in D, where p is a positive constant, then f is called a periodic function and the smallest such number p is called the period.
Determine the symmetry of the curve , compute .
The function is neither an even function nor an odd function.
Therefore, the given curve is no symmetrical about any of the axis.
Horizontal asymptotes: If either or , then the line y = L is a horizontal asymptote of the curve . If it turns out that, , then asymptote doesn’t exist to the right.
Vertical asymptotes: The line is a vertical asymptote if at least one of the following statements is true.
To obtain the horizontal asymptotes, compute .
Therefore, the given curve has no horizontal asymptote.
The function is undefined at .
Therefore, there is vertical asymptote at .
Intervals of Increase or Decrease:
Obtain the intervals of increase and decrease; compute the derivative of as follows
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