How do you graph #(x^2+3x-4)/x#?
1 Answer
Graph
Explanation:
A relatively easy approach is to
(1) notice that the function is not defined at
(2) at every other point in its domain the numerator can be divided by denominator getting
(3) graph the latter as a sum of two graphs
Graph of
graph{x+3 [-10, 10, -5, 5]}
Graph of
graph{-4/x [-10, 10, -5, 5]}
Summing these together, we see that around
Outside of the vicinity of point
All we have to find to position the graph more precisely is to find where it crosses the X-axis, that is where the function equals to zero.
This can be accomplished by solving a quadratic equation
Solutions are
That leads us to describe the behavior of the original function as follows.
As
As
After crossing the X-axis at point
At
As
Then the growth gradually becomes more linear and eventually follows approximately the straight line
The final graph looks like this
graph{x+3-4/x [-20, 20, -25, 25]}