Question

f(x)= 3(x-1)(x+2) / (x-4) (x+2)

c) State & plot removable discontinuities

d) State the y intercepts

Answer 1

Solution:

$f(x)=\dfrac{3(x-1)(x+2)}{(x-4)(x+2)}$

(c) This f(x) has a removable discontinuity at x=-2 as (x+2) can be cancelled out from numerator and denominator, but before that f(x) is in 0/0 form at x=-2.

(d) For y-intercepts, put x=0

$f(x)=y=\dfrac{3(x-1)(x+2)}{(x-4)(x+2)} \\\Rightarrow y=\dfrac{3(0-1)(0+2)}{(0-4)(0+2)} \\\Rightarrow y=\dfrac{-6}{-8}=\dfrac34$

Thus, y-intercept is $(0,\frac34)$