Is this a proper use of the word render?

Question

I'm writing a technical report and one of the sentences is:

Assuming otherwise would render A a function of B.

With the intention to say that if we would assume otherwise, A would be a function of B. Is this a proper use the word render, or should I use something align of:

Assuming otherwise results in A being a function of B.

Edit:

According to suggestions this might be better:

Without this assumptions A becomes a function of B.

Answer 1

The use of render here seems a bit inexact to me, especially if we take it literally to mean "cause to be or become," as in Wayfaring Stranger's definition above. Consider this assertion:

Assuming dachshunds are venomous would render Schnitzel [an imaginary pet dachshund] dangerous.

It seems to me that the conclusion of this sentence rather overstates the capacity of the assumption to transform Schnitzel into a life-threatening pet. The idea that the statement means to express is that making the initial assumption about dachshunds' venomousness would inevitably lead to a particular logical conclusion about Schnitzel's dangerousness, not that the simple act of making the assumption would cause that logical end result to be or become a fact in reality.

Logically, assuming venomousness does not cause dangerousness—and that would be true as a matter of logic even if we replaced dachshunds with diamondback rattlesnakes and "Schnitzel [an imaginary pet dachshund]" with "Tinkerbell [an imaginary pet diamondback rattlesnake]."

I can avoid the misleading aspect of my original assertion by rewording it along these lines:

If the assumption that dachshunds are venomous were true, Schnitzel would be dangerous.

Or this way:

If the assumption that dachshunds are venomous were adopted, it would logically follow that Schnitzel must be dangerous.

Or this way:

Under the assumption that dachshunds are venomous, Schnitzel would be dangerous.

Likewise in the OP's example, we could say

If any other assumption were adopted, A would logically have to be a function of B.

Or more simply,

Under any other assumption, A would be a function of B.

I realize that it is quite common to use render in the loose fashion that the OP's example does, but I would avoid it in this instance—in part because a technically more accurate alternative wording that omits render and yet doesn't sound especially stiff or formal is available, and in part because a technical report tracing the logical conclusions that follow from particular assumptions is likely to be held to an unusually high standard of accuracy and exactitude.