the basic function is f(x) = 1/x
the transformed function that I don't know how to graph is: y = f[(-1/3)x + 1]
The way you've written it implies which doesn't fit with the basic function.
I will assume you mean . It's best to do these in a series of steps.
For f(-x) reflect f(x) in the y-axis
For f(ax) increase 'steepness' by a. In this case it means it will come down from more sharply. You're not expected to know the exact shape but you should evaluate f(1) to get a set point. In your case the point will be
For f(x)+b you move the graph up the y axis by b. In your case b=1. This will also move any asymptotes.
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In your case you want the graph of 1/x:
- Reflected in the y-axis
- Steepened by a factor of 3 - passing through
- Moved up by 1 unit on the y-axis
See the graph attached for the final answer, I have included 1/x for comparison.