Homework Help

# Identify all holes, asymptotes, x-intercepts, y-ints of f(x) = 3x^2-12x+15/ x^2-9 also...

Student

Honors

• Up
• 1
• Down

Identify all holes, asymptotes, x-intercepts, y-ints of

f(x) = 3x^2-12x+15/ x^2-9

also include end behaviour analysis with a sketch that is a reasonable accurate representation of the function

Posted by mavig on April 3, 2012 at 5:22 AM via web and tagged with functions, math

College Teacher

(Level 3) Assistant Educator

• Up
• 1
• Down

The function is not defined for x=2

`lim_(xrarr2^+)f(x)=(-15/0^+)=-oo`

`lim_(xrarr 2^-)f(x)=(-15/0^-)=+oo`

One vertical asymptote: x=2

Degrre of the numerator is 2 more that the degree of the denominator therefore no oblique or horizontal asymptote.

y intercept is `f(0)=3/2`

x-intercept is for f(x)=0

iff (x+1)(2x^2-5x-3)=(x+1)((x-3)(2x-1))=0

3 x intercepts: `x=-1, x=3, x=-1/2`

Posted by cosinusix on April 3, 2012 at 11:05 AM (Answer #1)

Student

Honors

Honors

• Up
• 0
• Down

Sorry I meant the function of

f(x)= 2x^3 - 3x^2 - 8x -3 / x-2 = (x+1)(2x^2 - 5x -3)/x-2

Posted by mavig on April 3, 2012 at 5:26 AM (Answer #2)