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Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The...

Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The graph of f has a vertical asymptote at x=1, and f has a removable discontinuity at x=−2.

(a) Show that a=2 and b=−4.

(b) Find the value of c. Justify your answer.

(c) To make f continuous at x=−2, f(−2) should be defined as what value? Justify your answer.

(d) Write an equation for the horizontal asymptote to the graph of f. Show the work that leads to your answer.

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