Rigidity Review

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Notes

You can reference these sections to review.

• Chapter 3.1: Polynomial Functions
• Chapter 3.2: Rational Functions

Knowledge Checks

1. Sketch the quadratic polynomial \(f\) given by \[ f(x)=-3x^2+5x+7. \]
2. Identify the zeros and order of each zero of \(f\) where \(f\) is given by \[ f(x)=-4(x+6)^3(x+2)^4(x-2)^7(x-6)^8. \] Sketch all possible local behaviors at each zero by using only the order of each zero.
3. Determine the asymptotic behavior of the polynomial \(f\) given by \[ f(x)=-4(x+6)^3(x+2)^4(x-2)^7(x-6)^8. \]
4. Use the local and global behavior of a polynomial to sketch \(f\), where \(f\) is given by \[ f(x)=-4(x+6)^3(x+2)^4(x-2)^7(x-6)^8. \]
5. Identify the zeros and poles and the order of each zero and pole of \(f\) where \(f\) is given by \[ f(x)=\frac{x(x+7)^4}{(x-2)^6(x-5)^7}. \] Sketch all possible local behaviors at each zero by using only the order of each zero.
6. Take \(f\) to be the polynomial given by \[ f(x)=-9x^4(x+6)^8(x+2)^9(x-4)^2. \] Sketch \(f\) and use \(y\)-axis inversion to sketch \(g\), where \(g\) is given by \[g(x)=\frac{1}{-9x^4(x+6)^8(x+2)^9(x-4)^2}.\]
7. Use the global and local behavior of a rational function to sketch \(f\), where \(f\) is given by \[ f(x)=\frac{x(x+7)^4}{(x-2)^6(x-5)^7}. \]

• Knowledge Checks PDF
• Knowledge Checks Solutions

Remember, do the knowledge checks before checking the solutions.

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