^{2}+ (f(x)-3)). Replace f(x) by (3x)/(x-1) and simplify.

^{2}+ ((3x)/(x-1) - 3)).

q cannot be equal to x.

a) find the equations of the vertical and horizontal asymptotes of the graph of f.

the vertical and horizontal asymptotes to the graph of f intersect at the point Q(1,3)

b) find the value of q

c) the point P(x,y) lies on the graph of f. show that PQ = sqrt( ((x-1)^2) + ( (3)/(x-1) )^2 )

d) Find the coordinates of the points on the graph of f that are closest to (1,3)

Tutors, sign in to answer this question.

a) The vertical asymptote is the value of x such that x-q = 0(i.e. when the f(x)-> ∞.

Therefore, x = q.

The horizontal asymptote is the value of f(x) when x-> ∞.

Therefore, y = 3 (the ratio of the coefficients of x in f(x))

b) Since the these two lines intersect at Q(1, 3), the value of q = 1. (the value of x is the vertical asymptote and the value of y is the horizontal asymptote.

c) PQ = √((x-1)^{2} + (f(x)-3)). Replace f(x) by (3x)/(x-1) and simplify.

d) Minimize (x-1)^{2} + ((3x)/(x-1) - 3)).

I hope this helps.

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