Fair enough. Your question about the "whys" is a good one.

First, "function" in "the function f(x) = 4x-9" is not part of the name of the function, so it is not part of the technical expression.

Similarly, "sequence" in "a sequence t(n)" and "function" in "the function j(x)" are also not part of the NAME of the sequence or function.

Third, "slope" in "a line with slope 3/2" is not part of the technical expression, because a slope does not traditionally have a "proper name" like "Triangle ABC" or "Angle G"; a slope is a value and not a singular item.

Similarly, "x-intercept" in "x-intercept (4, 0)" is not part of a technical expression, because it does not work with the enclosed list to identify a singular item; "(4, 0)" does that by itself.

I am not ready to extrapolate universal rules from the above. But do the statements above make sense on their own, and will they help you to wade through material more comfortably?

–Kyle