Question: 2. Consider the rational function 8x + 20x 12 4x + 4x - 3 F(x) = (a) Factorise the numerator, f(x) = 8x +

$2. Consider the rational function [ F(x)=frac{8 x^{2}+20 x-12}{4 x^{2}+4 x-3} . ] (a) Factorise the numerator, ( f(x)=8 x$

2. Consider the rational function 8x + 20x 12 4x + 4x - 3 F(x) = (a) Factorise the numerator, f(x) = 8x + 20x 12, as much as possible. (b) Factorise the denominator, g(x) = 4x + 4x 3, as much as possible. (c) Write the factorised form of F, and then identify the Cartesian coordinates of any holes for y = F(x). (d) Find Cartesian coordinates of the x- and y-intercepts for y = F(x). (e) Apply polynomial long division to write the function F(x) in asymptotic form. = (f) Given your answer in (e) state the nature and equations of any asymptotes for y (g) State the domain and range of F. (h) Sketch the graph of y = F(x). Make sure all holes, axes-intercepts and asymptotes are clearly labelled. F(x).

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