Question 1146685
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Since you don't show the figure or the answer choices, you might take the trouble to rephrase the question....<br>
(1) Since the graph has no x-intercept, the numerator of the rational function has no variables; it is just a constant.<br>
(2) Note that (1) guarantees that the horizontal asymptote will be y=0.<br>
(3) Vertical asymptotes at x=-3 and x=4 mean there are factors of (x+3) and (x-4) in the denominator.<br>
(4) The factors of (x+3) and (x-4) in the denominator can be to any positive integer powers.  Different combinations of those powers will require different values of the constant in the numerator in order to make the graph pass through (3,1).<br>
Presumably only one of the answer choices shows only a constant in the numerator and factors of both (x+3) and (x-4) in the denominator.<br>
Here are the graphs of two functions that satisfy the given conditions.<br>
(a) {{{-6/((x+3)(x-4))}}}<br>
{{{graph(400,400,-5,5,-5,5,-6/((x+3)(x-4)))}}}<br>
(b) {{{36/((x+3)^2*(x-4)^2)}}}<br>
{{{graph(400,400,-5,5,-5,5,36/((x+3)^2*(x-4)^2))}}}<br>