How do you graph #y=(3x^2+10x-8)/(x^2+4)# using asymptotes, intercepts, end behavior?
2 Answers
See calculations below
Explanation:
The domain of y is
The denominator is
To find the intercepts, let
The y-intercept is
When
So,
The x-intercepts are
To calculate the limits when
So, the horizontal asymptote is
When
The curve cuts the horizontal asymptote at
To find the maximum and minimum, you have to calculate the derivative.
So we have 2 points,
We do a sign chart
graph{(y-(3x^2+10x-8)/(x^2+4))(y-3)=0 [-10, 10, -5, 5]}
x-intercepts
Explanation:
x-intercepts
By actual division,
It is evident that y = 3 is the horizontal asymptote that cuts the graph
at (2, 3)..
4.83,
nearly. These turning points are (-.93, -3.04) and (4.83, 4.04), nearly.
The graph justifies mini/max y at these points as -3.04/4.04,
nearly. y is bounded between these extremes.
graph{y(x^2+4)-3x^2-10x+8=0 [-16.29, 16.24, -8.13, 8.14]}