AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.5 Implicitly Defined Functions
Notes
An implicit relation like $x^2+y^2=25$ links $x$ and $y$ without solving for one. Its graph may fail the vertical line test, but parts of it can be functions.
Practice
Does $x^2+y^2=25$ define $y$ as a function of $x$?
$(3,4)$ and $(3,-4)$ are both on it.
The top half of $x^2+y^2=25$ as a function:
Positive square root.
The point $(1,2)$ is on $x^2+xy=c$ when $c=$
$1+2$.
Ready for more? Take the Unit 4 test.