The phrase "a function of the extent" is correct and usable in written English.
It can be used in contexts where you are discussing how one variable or factor depends on or is influenced by the degree or level of another variable.
Example: "The success of the project is a function of the extent to which team members collaborate effectively."
Alternatives: "depends on the degree" or "is determined by the level".
We have analyzed in detail the fracture mechanisms of the nanostructures under tension as a function of the extent of interlayer bonding through chemical functionalization.
His strong implication is that an orchestra's greatness is a function of the extent to which it embraces modernism.
The stretched/oriented films were compared for their water vapor transport and optical properties as a function of the extent of orientation (i.e., draw ratio, DR).
Some researchers may consider R2 a measure of model performance rather than model-data-fit as a function of the extent to which underlying assumptions of HLM are met.
In our study, this error was expressed as a function of the extent (P/N) in which the reactant concentrations deviated from the stoichiometric ratio of each oxidation reaction.
The activation energy is estimated by means of both integral (Starink) and differential (Friedman) isoconversional methods, as a function of the extent of conversion, corresponding to the identified reaction intervals.
The formation of trans-isomers however, appears to be a function of the reaction extent only.
These models aim to estimate and correlate strain energy release rate and the residual stiffness as a function of the damage extent.
The habitat suitability of a shorebird metapopulation is studied as a function of the scale (extent) and resolution (grain-size) of the environmental covariates with a maximum entropy species distribution model (MaxEnt) for integration with climate change simulations.
Census designs using non-contiguous plots are useful for sampling large regions, but their interpretation is not straightforward because species number is a function of the spatial extent of the landscape and the size of the sample units.
The amount of water required by residential landscaping is a function of the areal extent of residential landscaping (i.e. tree/shrub or turf grass), the water-loss rate for different landscaping types, the efficiency with which the landscape is irrigated, and local climatic factors (i.e. reference evapotranspiration and precipitation) (Lowry et al. 2011).
