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Magazine Problem 3
How do you know when a polynomial is factored completely?
Problem 3
In Exercises 3-6, describe the transformation of \(f\) represented by \(g\). Then graph each function. (See Example 1. ) f(x)=x^4, g(x)=x^4+3
Problem 5
In Exercises 3-6, describe the transformation of \(f\) represented by \(g\). Then graph each function. (See Example I.)\(f(x)=x^5, g(x)=(x-2)^5-1\)
Problem 6
\(f(z)=-7 z^4+z^2-25\)
Problem 7
Solve the equation. \(5 w^3=50 w\)
Problem 7
Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.$$ \begin{array}{|l|c|c|c|c|c|c|} \hline \boldsymbol{x} & -6 & -3 & 0 & 3 & 6 & 9 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & -2 & 15 & -4 & 49 & 282 & 803 \\ \hline \end{array} $$
Problem 7
ANALYZING RELATIONSHIPS In Exercises 7鈥�10, match the function with the correct transformation of the graph of f. Explain your reasoning.\(y=f(x-2)\)
Problem 8
Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.$$ \begin{array}{|l|c|c|c|c|c|c|} \hline \boldsymbol{x} & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & -14 & -5 & -2 & 7 & 34 & 91 \\ \hline \end{array} $$
Problem 9
Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.\((-4,-317),(-3,-37),(-2,21),(-1,7),(0,-1)\) \((1,3),(2,-47),(3,-289),(4,-933)\)
Problem 10
Use finite differences to determine the degree of the polynomial function that fits the data. Then use technology to find the polynomial function.\((-6,744),(-4,154),(-2,4),(0,-6),(2,16)\) \((4,154),(6,684),(8,2074),(10,4984)\)
