2 Fill in the following information about fa Graph fx Be sur

2. Fill in the following information about f(a). Graph f(x). Be sure to label the graph. If there are none, please print \"NONE 3r-103x-10 holes:nok x-intercept(s) y-intercept vertical asymptote(s): horizontal asymptote domain:9 lo 2-

Solution

f(x) = (2x²-72)/(x²-3x-10) = 2(x+6)(x-6)/(x-5)(x-2)

hole-none

x intercept, f(x)=0

2(x+6)(x-6)=0

x+6=0, x-6=0

x=-6,6

x intercept (-6,0),(6,0)

y intercept, x=0

f(x)= -72/-10=7.2

y intercept (0,7.2)

verical asymptote

(x-5)(x+2)=0

x-5=0, x+2=0

x=5, -2

horizontal asymptote

numerator\'s degree= denominator\'s degree

therefore

y= ratio of numerator and denominator\'s leading coefficient

y=2/1=2

Domain

Restriction is at vertical asymptote

(-infinity,-2)U(-2,5)U(5,infinity)