Textbook 11.3 exercises

Exercise 11.1. Find the domain, The vertical asymptotes and removable discontinuities of the function.

Question b) (x^2+2)/(x^2+6x+8)

step 1: To find the domain we need to to set the denominator to zero

  1. (x^2+6x+8)=0

step 2: We solve by factoring the equation to its simplest form.

2. (x+4)=0 and (x+2)=0

step 3: We solve both equations to get x by its self.

3. x=-4  and x=-2

step 4: Both -4 and -2 are the restrictions that makes the denominator zero.

4. D: {R|x not equal -4,-2}

step 5: By using the restrictions on the domain we are able to find the vertical asymptote.

5. The graph does not pass through the values of -4  and -2

step 6:  To find the removable discontinuities you need to see if the equation has any factorable polynomials.

6: Since none of the polynomials can be factored then the equations has no removal discontinuities.

P.S: Sorry for any errors