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(4) Let S :P+P be the function which sends p(x) to p(x+1); that is, it replaces...

(4) Let S :P+P be the function which sends p(x) to p(x+1); that is, it replaces each occurrence of a in p(x) with r +1. (a) C

(4) Let S :P+P be the function which sends p(x) to p(x+1); that is, it replaces each occurrence of a in p(x) with r +1. (a) Compute S(x²) and S(q? - 1+1). (b) Plot y = r2 and y= 2). (e) Can you describe what S does to the graph of a polynomial? (d) Show that S is a linear transformation, by showing it preserves addition and it preserves scalar multiplication.
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4/6) S (*) Here Þ(2) = x (say) i s (P(X) Þa+1) (2+1)? S (2) = (x+1) = Here 9(2) S*+1) 960) = -x+! (say) :: S() = q (u+1) (2+: S(x-x+1)=X+2+1 4) b) plot y=X First, we y ♡ 7x (0,0) Then he plot s(%) lie, y- (uti) J ar (-1,0) parabola represents (4) B- Þ(+) + (x+1) [using the properties of polynomials] os (pca)) + s (~(+1)) tence S preserves addition ü) net and p be a a sca

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