Question

This graph represents the function f(x) = x^2 - 4x + 3/ x^2 + ax + b. a= ___ b= ___

Answer 1

f(x) = (x+2)(x-8)/(x-6)(x+4) <-> x=6,x=-4

i(x) = (x-4)(x-6)/(x-2)(x+8) <-> x=2,x=-8

k(x) = (x-2)(x+8)/(x+6)(x-4) <-> x=-6,x=4

m(x) = (x+4)(x-6)/(x+2)(x-8) <-> x=-2,x=8

Explanation:

The function is discontinuous if the denominator is zero.

We will check for which function the values are given

1) f(x) = (x+2)(x-8)/(x-6)(x+4)

if x = 6 and x = -4 the denominator is zero

So, x=6 and x=-4 given

2) g(x) = (x+4)(x-8)/(x+2)(x-6)

if x = -2 and x = 6 the denominator is zero

So, x= -2 and x= 6 not given so, g(x) will not be considered

3) h(x)= (x+2)(x-6)/(x-8)(x+4)

if x = 8 and x = -4 the denominator is zero

So, x= 8 and x= -4 not given so, h(x) will not be considered

4) i(x) = (x-4)(x-6)/(x-2)(x+8)

if x = 2 and x = -8 the denominator is zero

So, x= 2 and x= -8 given

5) j(x) = (x-2)(x+6)/(x-4)(x+8)

if x = 4 and x = -8 the denominator is zero

So, x= 4 and x= -8 not given so, j(x) will not be considered

6) k(x) = (x-2)(x+8)/(x+6)(x-4)

if x = -6 and x = 4 the denominator is zero

So, x= -6 and x= 4 given

7) l(x) = (x-4)(x+8)/(x+6)(x-2)

if x = -6 and x = 2 the denominator is zero

So, x= -6 and x= 2 not given so, l(x) will not be considered

8) m(x) = (x+4)(x-6)/(x+2)(x-8)

if x = -2 and x = 8 the denominator is zero

So, x= -2 and x= 8 given