graph of function

the graph of a function $\text{[math]}$ is the set of points $\text{[math]}$ such that $\text{[math]}$ . it is denoted $\text{[math]}$ .
[cite:@calc_hubbard_2015 definition 3.1.1]

thus the graph of a function $\text{[math]}$ lives in a space whose dimension is the sum of the dimensions of the domain and codomain of $\text{[math]}$ .
it is convenient to denote a point in the graph of a function $\text{[math]}$ as $\text{[math]}$ . with $\text{[math]}$ and $\text{[math]}$ . but this presupposes that the "active" variables are the first variables, which is a problem, since we usually cannot use the same active variables at all points of the mainfold.
[cite:@calc_hubbard_2015]

the graph of a partial function $\text{[math]}$ is the relation $\text{[math]}$ 2. partial functions $\text{[math]}$ and $\text{[math]}$ are equal, $\text{[math]}$ , if $\text{[math]}$ .

[cite:;taken from @computability_soare_2016 definition 2.1.7]