Question

Use complete sentences to analyze the graph of the function f(x) = log 1/3 x.

Part 1: Describe the domain, range, and general shape of this graph.

Part 2: Using complete sentences, explain how plotting specific points helps graph the function and note any critical points such as its intercepts.

Okay so I have part one down since that was basically the easy part. But the second part is what i'm having trouble with. I'm sure I haven't read anything about this in the lesson. I even tried going back and I went through all of the sections in the chapter. Can anyone explain?

Answer 1

\[f(x)=\log \frac{ 1 }{ 3 }x\]?

Answer 2

Yea! The line goes through (0, 0) diagonally going left to right and decreases. Kind of like this but less....you know.

Answer 3

Are you sure that's the graph? I get something different.
If you know the domain (all possible #s for the x that you can plug into the function of x), then you can get the range (all the y values for x)
Using that info you plot can plot your points on the graph
The critical point here is where your line intersects the x-axis.
Also important is where it doesn't intersect because if x value were a negative number your number would be a non-real # & DNE, therefore doesn't cross the y-axis

Answer 4

We have a program called geogebra and the format we have to use to graph it is f(x)=lg(1/3)x. It comes out looking like that. The drawing isn't 100% accurate it's just an example of what the line is doing in the graph.