sketch the graph of f(x)=x^2+2x-8/x^2+6x+8 lim f(x) x -->-4

Question

limit of f(x) x extends to -4.

Answer 1

The polynomial function is  .

Here we have to graph 

Graph the polynomial using following points.

1. Simplify the polynomial if possible.

  

2. Find and plot the y-intercept  by evaluating .

      

3. Find the zeros of the numerator by solving the equation. Then plot the corresponding x-intercepts.

  

4. Find the zeros of the denominator (if any) by solving the equation. Then sketch the corresponding vertical asymptotes.

  

5. Horizontal asymptote determined by comparing the degrees of numerator and denominator.

For this rational function, the degree of the numerator (n = 1) is equal to the degree of the denominator (m = 1).

So, the ratio of leading coefficient of the numerator and denominator correspondingly gives

the horizontal asymptote i.e .

So the graph has the line as a horizontal asymptote.

Continues...

Answer 2

 

6. Plot at least one point between and one point beyond each x-intercept and vertical asymptote.

x
2
0
-2
-3
-4
-5

7. Plot the points and graph the polynomial and asymptotes.

From the graph we can conclude that when x approaches to -4, .

So, .