Question

a function is a relation where every input has a exactly one output. the ____________ is all the inputs (the x - values you are allowed to put into the function). the __________ is all the outputs (the y - values get out of the function). example 1: numerical functions a) relation: ((1, 9), (2, 13), (3, 15), (4, 15), (5, 12), (6, 10)) domain: __________ range: __________ is it a function? __________ (are there any repeat x - values?) b) relation: ((1, 1), (2, 3), (2, 5), (4, 7), (5, 6)) domain: __________ range: __________ is it a function? ____________ (are there any repeat x - values?) example 2: graphic functions to help understand this definition, look at the function below, which relates the time of day to the temperature. set a is the domain. inputs: 1, 2, 3, 4, 5, 6 set b contains the range. outputs: 9, 10, 12, 13, 15

Explanation:

Step1: Recall function - domain and range definitions

The set of all inputs of a function is called the domain, and the set of all outputs is called the range.

Step2: Analyze relation a)

For relation \((1,9),(2,13),(3,15),(4,15),(5,12),(6,10)\):
The domain is the set of all \(x -\)values. So, Domain: \(\{1,2,3,4,5,6\}\).
The range is the set of all \(y -\)values. So, Range: \(\{9,10,12,13,15\}\).
Since each input has exactly one output, Is it a function? Yes.

Step3: Analyze relation b)

For relation \((1,1),(2,3),(2,5),(4,7),(5,6)\):
The domain is the set of all \(x -\)values. So, Domain: \(\{1,2,4,5\}\).
The range is the set of all \(y -\)values. So, Range: \(\{1,3,5,6,7\}\).
Since the input \(x = 2\) has two outputs (\(y=3\) and \(y = 5\)), Is it a function? No.

Answer:

The first blank is "domain".
The second blank is "range".
Example 1 a) Domain: \(\{1,2,3,4,5,6\}\), Range: \(\{9,10,12,13,15\}\), Is it a function? Yes.
Example 1 b) Domain: \(\{1,2,4,5\}\), Range: \(\{1,3,5,6,7\}\), Is it a function? No.