ok so I have three questions I am struggling with.
1.) The table of values represents a polynomial function f (x).
How much greater is the average rate of change over the interval [7, 9] than the interval [4, 6]?
x f(x)
4 358
5 690
6 1178
7 1852
8 2742
9 3878
2.) What is (f+g)(x)?
f(x)= x3 - x
g(x)= x3+2x2-10
3.)
What is (f⋅g)(x)?
f(x)=x2+2x−6
g(x)=x4+3
+6248 \(\bar{\Delta}_{[7,9]} = \dfrac{3878-1852}{9-7} = 1013\\ \bar{\Delta}_{[4,6]} = \dfrac{1178-358}{6-4}=410\\ \bar{\Delta}_{[7,9]}-\bar{\Delta}_{[4,6]} = 1013-410 = 603\)
\(f(x) = x^3-x\\ g(x) = x^3+2x^2-10\\ (f+g)(x) = f(x) + g(x) = 2x^3 +2x^2 - x - 10\)
\(f(x) = x^2+2x-6\\ g(x) = x^4+3\\ (f-g)(x) = f(x)-g(x) = -x^4+x^2+2x-9\)
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