What is the graph of the function f(x)= f(x)=-x^2-9x-20/x+4?

Synthetic division? You’ll make the positive 4 a negative then set it up as a long division except you only put the numbers and not the x’s. So it would be -4 division sign then on the right of the line is -1 -9-20. Then you bring the -1 down and multiply -4 by -1 which would be 4 and you put it under -9 then do the simple math for those then bring the -5 down to the right of the negative 1. Then multiply negative 4 by negative 5 which is positive 20. So your answer wouldn’t have a remainder. So it would be -x-5

isyllus isyllus · Answer 2 · 2019-07-16T06:59:45+02:00

Answer:

Graph in attachment

Step-by-step explanation:

Given: [tex]f(x)=\dfrac{-x^2-9x-20}{x+4}[/tex]

We need to draw the graph of rational function f(x).

First we find the x and y intercept of f(x)

For x-intercept: put f(x)=0

[tex]\dfrac{-x^2-9x-20}{x+4}=0[/tex]

[tex]-x^2-9x-20=0[/tex]

[tex](x+5)(x+4)=0[/tex]

[tex]x=-5[/tex]

For y-intercept: Put x=0

[tex]f(0)=\dfrac{0^2-9\cdot0-20}{0+4}[/tex]

[tex]f(0)=-5[/tex]

For vertical asymptote: Set denominator to 0

[tex]x+4=0[/tex]

But x+4 is common factor at numerator and denominator.

So, x=-4 will be hole of the graph.

Hole: x=-4

Using above information to draw the graph.

Please find attachment for graph.