Question

if the graph shows a function.
(1) input = 1: exactly one output, which is 2
(2) input = 2: exactly one output, which is 1
(3) input = 3: more than one output
(4) input = 4: exactly one output, which is 3
(5) decide if the graph shows a function by answering both questions.
(6) does each input have exactly one output?
?
does the graph show a function?
?
graph with x-axis from 0 to 5 and y-axis from 0 to 5, with points at (1,2), (2,1), (3,2), (3,3), (4,3)

Explanation:

Step1: Recall function definition

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

Step2: Analyze input = 3

For input \( x = 3 \), there are two output values (y - values: 2 and 3) as seen from the graph (points at (3, 2) and (3, 3)). So not every input has exactly one output.

Step3: Determine function status

Since the definition of a function requires each input to have exactly one output, and here input \( x = 3 \) has more than one output, the graph does not represent a function.

Answer:

Does each input have exactly one output? No
Does the graph show a function? No