Find traits and sketch the graph the equation for a function $ g(x) $ that shifts the function \[f(x) = \frac{x-3}{x^2+2x-3}\]one unit to the left. **Label and scale your axes.**

The given function is: f(x)=x-3x2+2x-3 =x-3x2+3x-x-3 = x-3x(x+3)-1(x+3) f(x)=x-3(x+3)(x-1)…

Answered: Find traits and sketch the graph the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Find traits and sketch the graph the equation for a function $ g(x) $ that shifts the function

\[
f(x) = \frac{x-3}{x^2+2x-3}
\]

one unit to the left. **Label and scale your axes.**

Expert Solution

Step 1

The given function is:

$f (x) = \frac{x - 3}{x^{2} + 2 x - 3} = \frac{x - 3}{x^{2} + 3 x - x - 3} = \frac{x - 3}{x (x + 3) - 1 (x + 3)} f (x) = \frac{x - 3}{(x + 3) (x - 1)}$

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