Let x1, x2, and x3 be distinct real numbers such that x1

(a) Show that T is a linear transformation.
(b) Show that T is one-to-one.
(c) Verify that if a1, a2, and a3 are any real numbers, then

Where

(d) What relationship exists between the graphs of the function
a1P1(x) + a2P2(x) + a3P3(x)
and the points (x1, a1), (x2, a2), and (x3, a3)?

Transcribed Image Text:

p(xi) T(p(x)) = | p(x2) p(x3) αι a3 (x-x2) (x-x2) P3(x) =-(a-na-w P3(x) = P (x)= (x2-x1)(x2-r ) 2-*1)(x2-x3 3-X1) (X3-X2)