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Practice variation 3 of 3

Graph transformations — Turning points from components

Your question

Suppose is strictly increasing and is strictly decreasing. Which can their sum still have?

A local maximum (if the decrease of dominates then loses)
No turning points ever
Only discontinuities
Infinitely many vertical asymptotes forced by the sum alone

This practice question was inspired by Question 4 in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

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