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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 62 (page 226)

Make up a rational function that has $y = 2 x + 1$ as an oblique asymptote. Explain the methodology that you used.

Short Answer

Expert verified

The rational function $\frac{6 x^{2} + x - 1}{3 x - 1}$ which is having $2 x + 1$ as an oblique asymptote.

Step by step solution

01

Step 1 Let us assume a function,

$f (x) = \frac{a x^{m} + b x^{m - 1} + . . . . + k}{a_{1} x^{p} + b_{1} x^{p - 1} + . . . . + k_{1}}$

Let us multiply the given function by $(2 x + 1)$ .

$\frac{a x^{m} + b x^{m - 1} + . . . . + k}{a_{1} x^{p} + b_{1} x^{p - 1} + . . . . + k_{1}} (2 x + 1)$

02

Step 2 So as the multiplied and divided polynomial can take any value.

So, let us take any function like $3 x - 1$ after multiplication and division it will be as such $\frac{6 x^{2} + x - 1}{3 x - 1}$ .

Hence this function can be taken as one of the polynomial function having $2 x + 1$ as its oblique asymptote.

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