Question

which scenario best represents the graph?
a the student starts swimming at a fast rate, stops and treads water, then swims at a slower rate.
b the student starts swimming at a fast rate, transitions to a slower rate, then stops swimming.
c the student starts swimming at a slow rate, accelerates to a faster rate, then swims at a slower rate.
d the student swims at the same, fast rate for the entire swim.

1. consider the table.

which statement is true?

x	y
-10	-10
2	9
-4	1
7	0
2	-6

a the table is a function because for each input value, there is exactly one output value.
b the table is a function because for the input value of 2, there is more than one output value.
c the table is not a function because for each input value, there is exactly one output value.
d the table is not a function because for the input value of 2, there is more than one output value.

Explanation:

Step1: Recall the definition of a function

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

Step2: Analyze the table

Looking at the table, when \(x = 2\), we have two different \(y\) - values: \(y=9\) and \(y = - 6\). This means that for the input value \(x = 2\), there is more than one output value.

Step3: Evaluate each option

• Option A: The table is not a function (because of the repeated \(x\) - value with different \(y\) - values), so A is incorrect.
• Option B: The table is not a function, so B is incorrect.
• Option C: The table is not a function, so C is incorrect.
• Option D: Since for \(x = 2\) (input value) there are two different \(y\) - values (output values), the table is not a function. So D is correct.

Answer:

D. The table is not a function because for the input value of 2, there is more than one output value.