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The phrase "a function of a shift in" is correct and usable in written English.
It can be used to describe how one variable or phenomenon is influenced or determined by a change in another variable or phenomenon.
Example: "The increase in sales is a function of a shift in consumer preferences towards eco-friendly products."
Alternatives: "a result of a change in" or "an outcome of a transition in".
Exact(2)
John Longman, president of acoustic consultant firm Longman Lindsey, told me that he thinks the rise in complaints is a function of a shift in the zeitgeist.
We hypothesized that, while locomotor activity shifted, the circadian pattern of serum OT rhythms would not change as a function of a shift in the light cycle.
Similar(58)
But it also is a function of a larger shift in the climate.
That is, authority for action shifts to lower levels in the hierarchy, as a function of shifts in access to information.
Decreasing fecundity at the highest densities may be the result of a shift in sex allocation towards the male function.
Core level electronic spectra taken as a function of semiconductor doping reveal shifts in binding energy attributed to molecular bonding.
Figure 2 (A) Absorption shift of dye solution as a function of dielectric constant in non-hydrogen-bond donating solvents, (B) Absorption shift of dye solution as a function of dielectric constant in hydrogen bonding solvents.
The theory already presented allows plotting sample size as a function of mean difference, albeit with a shift in algorithm.
The H chemical shifts of these crosspeaks are plotted as a function of pH in Figure 6a, and the C chemical shifts are plotted in Figure 6b.
The shift was partly a function of steep budget cuts in the 1970's, but it also reflects a change in educational philosophy.
The resulting shifts as a function of Θ are shown in Fig. 9 (c).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com