Example 8 from Algebra and Trigonometry, 6.4 Graphs of Logarithmic Functions

Graphing a Reflection of a Logarithmic Function

Sketch a graph of $f (x) = \log (- x)$ alongside its parent function. Include the key points and asymptote on the graph. State the domain, range, and asymptote.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Before graphing $f (x) = \log (- x),$ identify the behavior and key points for the graph.
- Since $b = 10$ is greater than one, we know that the parent function is increasing. Since the input value is multiplied by $−1,$ $f$ is a reflection of the parent graph about the y-axis. Thus, $f (x) = \log (- x)$ will be decreasing as $x$ moves from negative infinity to zero, and the right tail of the graph will approach the vertical asymptote $x = 0.$
- The x-intercept is $(−1, 0) .$
- We draw and label the asymptote, plot and label the points, and draw a smooth curve through the points.
Figure 14

The domain is $(- \infty, 0),$ the range is $(- \infty, \infty),$ and the vertical asymptote is $x = 0.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Graph $f (x) = - \log (- x) .$ State the domain, range, and asymptote.

How did it go?

Solution

Your turn

Solution

Your turn