httppuushyapLD40115d1abfpng Can you solve a and b How can yo

http://puu.sh/yapLD/40115d1abf.png

Can you solve a and b?

How can you determine the difference between a rational function being undefined because of a vertical
asymptote and being undefined because of a hole?

Solution

f(x)=(x²-3x+2)/(x-2)

= (x-2)(x-1)/(x-2)

Here x-2 is common in numerator and denominator

So the function is undefined at x=2 because of hole

g(x)=(x³-2x²)/(x-2)

=(x²(x-2)/(x-2)

Here again x-2 is common in numerator and denominator so the function is undefined at x=2

h(x)=(x-3)/(x-2)

Here we dont have anything common. So we set the denominator to 0

x-2=0

x=2

So the vertical asymptote is x=2

k(x)=(x⁴-8x-16)/(x-2)

Here nothing is common

So we set the denominator to 0

x-2=0

x=2

So the vertical asymptote is x=2

b. f(x)=1/(x+1)

g(x)=(x²+3x+2)/(x+1)