Question

a) input = 1: exactly one output, which is 2
b) input = 2: exactly one output, which is 3
c) input = 3: exactly one output, which is 3
d) input = 4: exactly one output, which is 4

e) decide if the graph shows a function by answering both questions.
f) does each input have exactly one output?
?
does the graph show a function?
?

Explanation:

Step1: Recall function definition

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

Step2: Analyze the graph's x - values

Check each x - value (input) in the graph:

• For \(x = 1\), the point is \((1,2)\), so output is 2 (one output).
• For \(x = 2\), the point is \((2,3)\), so output is 3 (one output).
• For \(x = 3\), the point is \((3,3)\), so output is 3 (one output).
• For \(x = 4\), the point is \((4,4)\), so output is 4 (one output).
• For \(x = 5\), the point is \((5,4)\), so output is 4 (one output).

Each input (x - value) has exactly one output (y - value).

Step3: Determine if it's a function

Since each input has exactly one output, by the definition of a function, the graph represents a function.

Answer:

For "Does each input have exactly one output?": Yes
For "Does the graph show a function?": Yes