cracking by heating to a very high temperature is an example of what type of reaction?

Cracking by heating to a very high temperature is an example of a decomposition reaction, more specifically a thermal decomposition (often called thermal cracking in organic chemistry).

Quick Scoop: The Core Idea

• In cracking, large hydrocarbon molecules break down into smaller, simpler molecules when strongly heated.
• Because one large substance splits into several simpler substances, this fits the definition of a decomposition reaction.

• When the decomposition is driven specifically by heat, it is called thermal decomposition (or pyrolysis in many organic/industrial contexts).

So, the best, exam-style answer to:

“Cracking by heating to a very high temperature is an example of what type of reaction?”

is:

It is a decomposition reaction (thermal decomposition / thermal cracking).

Tiny Story To Remember It

Imagine a very long chain made of many identical links (a long-chain hydrocarbon).
You heat the chain so intensely that some of the links snap, breaking it into several shorter chains and pieces. Nothing “new” is added from outside; you’re just breaking one big thing into smaller ones.
That picture is exactly what happens in cracking: a single complex substance breaks into several simpler ones, which is why it’s classified as a decomposition reaction.

Information gathered from public forums or data available on the internet and portrayed here.

TL;DR: Cracking by strong heating = decomposition reaction, specifically thermal decomposition (thermal cracking).