Question

8.26 true/false tuesday

1. true or false: a relation is a function if each input has more than one output.
2. true or false: in a function, it is okay for the y - values to repeat.
3. true or false: in a mapping diagram, an x - value can have two arrows mapping from it.

Explanation:

Step1: Recall function definition

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze statement 1

If each input has more than one output, it is not a function. So, the statement "A relation is a function if each input has more than one output" is False.

Step3: Analyze statement 2

In a function, y - values can repeat. For example, in the function $y = x^{2}$, when $x = 2$ and $x=- 2$, $y = 4$. So, the statement "In a function, it is okay for the y - values to repeat" is True.

Step4: Analyze statement 3

In a mapping diagram, if an x - value has two arrows, it means it is mapped to two different y - values. A function requires each x - value to have exactly one y - value. So, an x - value cannot have two arrows in a function mapping diagram. The statement "In a mapping diagram, an x - value can have two arrows" is False.

Answer:

1. False
2. True
3. False