How to sketch the graph of $y = \frac{g(x)}{f(x)}$?
This diagram shows the graphs of the functions $y = f(x)$ and $y = g(x)$.
The question is -
Sketch the graph of $y = \frac{g(x)}{f(x)}$.
Indicate clearly where the y-intercept, the x-intercepts, and any asymptotes occur.
I have been working on this problem for almost an hour and can't figure out how to sketch the graph. Any help would be highly appreciated.
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$\begingroup$If I am correct, the question is asking you to sketch the graph in the same paper.
to sketch $\frac{f(x)}{g(x)}$ , see the corresponding values, i.e output
At x = 0, we can see that $f(x) = -4$ and $g(x) = -2$ $\implies$ $\frac{f(x)}{g(x)} = 2 $
Now, Mark the point (0,2) on the graph sheet. Similarly for the points at $ x = 8 $ and at the points where they have same output which is at $ f(x) = g(x) = -2 $ and at $f(x) = g(x) = -1 $
Join all the points and you have the graph of $\frac{f(x)}{g(x)}$
y-intercept is where the graph cuts the y-axis which is at x=0 and hence y-intercept = 2
The graph cuts x-axis when $\frac{f(x)}{g(x)} = 0 \implies f(x) = 0 $ so, it will be in between x = 3 and x = 4
the graph has an asymptote when $g(x) = 0$ which is somewhere in between x = 6 and x = 7
Hope this helps.
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