Use a graphing utility to compare the graphs of y1 and y2. y1 = 3x3 5x2 + 4x 5 2x2 6x +

Chapter 3, Problem 55

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Exploration Use a graphing utility to compare the graphs of \(y_{1}\) and \(y_{2}\).

\(y_1=\frac{3x^3-5x^2+4x-5}{2x^2-6x+7},\quad\ \ y_2=\frac{3x^3}{2x^2}\)

Start with a viewing window of \(-5 \leq x \leq 5\) and \(-10 \leq y \leq 10\), and then zoom out. Make a conjecture about how the graph of a rational function f is related to the graph of \(y=a_{n} x^{n} / b_{m} x^{m}\), where \(a_{n} x^{n}\) is the leading term of the numerator of f and \(b_{m} x^{m}\) is the leading term of the denominator of f.

Text Transcription:

y_1

y_2

y_1 = 3x^3 - 5x^2 +  4x - 5 / 2x^2 - 6x + 7,   y_2 = 3x^3 / 2x^2

-5 leq x leq 5

-10 leq y leq 10

y = a_n x^n / b_m x^m

a_n x^n

b_m x^m