4.7

Topic

Parametrization of Implicitly Defined Functions

Practice by unit: Functions Involving Parameters, Vectors, and Matrices

Sub-standards

• 4.7.A.1 — Represent a curve in the plane parametrically. A parametrization (x t( ), y t( )) for an implicitly defined function will, when x(t) and y t( ) are substituted for x and y, respectively, satisfy the corresponding equation for every value of t in the domain.
• 4.7.A.2 — If f is a function of x, then y = f (x) can be parametrized as (x t( ), y t( )) ( = t f , ( )t ). If f is invertible, its inverse can be parametrized as(x t( ), y t( )) ( = f t( ), t) for an appropriate interval of t.
• 4.7.B.2 — An ellipse can be parametrized using the trigonometric functions x( )t h = + acost and y t( ) = + k bsin t for 0 t 2 .