# Science:Math Exam Resources/Courses/MATH307/December 2010/Question 03 (a)

MATH307 December 2010
Other MATH307 Exams

### Question 03 (a)

Suppose we are given 4 points (x1, y1), (x2, y2), (x3, y3) and (x4, y4) in the plane and we want to find a function ƒ(x), defined for ${\displaystyle x_{1}\leq x\leq x_{4}}$, whose graph interpolates these points. Assume that

${\displaystyle f(x)={\begin{cases}p_{1}(x)&{\text{for }}x_{1}\leq x\leq x_{2}\\p_{2}(x)&{\text{for }}x_{2}\leq x\leq x_{3}\\p_{3}(x)&{\text{for }}x_{3}\leq x\leq x_{4}\end{cases}}}$

where each pi(x) is a polynomial.

(a) What equations, written in terms of pi(x) and possibly their derivatives, express the condition that ƒ(x) goes through the given points? Do the equations imply that ƒ(x) is continuous?

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