Question

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

Answer 1

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

Answer 2

Answer:

Graph in attachment

Step-by-step explanation:

Given:  $f(x)=\dfrac{-x^2-9x-20}{x+4}$

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

$\dfrac{-x^2-9x-20}{x+4}=0$

$-x^2-9x-20=0$

$(x+5)(x+4)=0$

$x=-5$

For y-intercept: Put x=0

$f(0)=\dfrac{0^2-9\cdot0-20}{0+4}$

$f(0)=-5$

For vertical asymptote: Set denominator to 0

$x+4=0$

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.