How do you graph #y=-5/x-7# using asymptotes, intercepts, end behavior?
1 Answer
See below:
Explanation:
We immediately notice that if our denominator is equal to zero, we'll be undefined and have a vertical asymptote at
Since we have a vertical asymptote, this means the graph never intercepts the
What about
Adding
Let's multiply both sides by
Dividing both sides by
This is where our graph intercepts the
Since we know our function has a vertical asymptote, we know it goes unbounded towards infinity. What about negative infinity?
Let's evaluate the following limit:
Since we will be dividing by a more and more negative number,
Putting together all we know about our function, we can graph!
graph{-5/x-7 [-9.71, 10.29, -10.42, 0]}