# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [Multivariable real-valued function: coefficient order, declared domain, slices and point values of a bivariate quadratic](/en/derivations/derivation-mko-multivariable-real-function-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-multivariable-real-function)

The coefficient vector in the order [1,x,y,x²,xy,y²] is c=(1,−2,3,1,2,−1), and the declared domain is the closed rectangle R=[−1,2]×[0,3]. (1) Write f and confirm that f:R→ℝ is a function; (2) check the x and y bounds separately to decide whether (2,3), (3,1), (0,−1) lie in R; (3) compute f(2,1) and f(1,2), and prove that g, obtained by swapping the x and y coefficients, is a different function; (4) find the x-slice at y=1 and show that neither the given y=1 slice nor the four specified point values determine f.

Multivariable real-valued function

derivation-mko-multivariable-real-function-01





1 1 results · Page 1 of 1