Final answer:
The question deals with the concept of a mathematical function, which is a specific type of relation where each input is associated with exactly one output. The problem statement exemplifies that when an input corresponds to multiple outputs, it does not qualify as a function. Additionally, the answer discusses the rules for addition, subtraction, multiplication, and division, including how to handle operations with positive and negative numbers.
Step-by-step explanation:
Understanding Functions and Mathematical Operations
The statement 'Not a function - there is an input (4) that goes to two different outputs (5 and -5)' refers to the definition of a function in mathematics. A function is a relation that assigns exactly one output for each input. Therefore, if an input corresponds to more than one output, it can't be called a function.
When it comes to basic arithmetic operations, there are specific rules. For addition, when two positive numbers are added, such as 3+2, the result is a positive number, 5. Conversely, adding two negative numbers, like -4 + (-2), also produces a negative result, -6. However, when you add numbers with different signs, you subtract the smaller number from the larger and use the sign of the larger number. The same logic applies to subtraction by changing the sign of the number being subtracted and then adding, as in 5 - (+3) = 2.
For multiplication and division, the rules are similar. Multiplying two positive or two negative numbers results in a positive output. Multiplying numbers with opposite signs gives a negative result. The same sign rules apply when dividing numbers.