Question

select the correct answer.
which of the following represents a function?
a.
graph of coordinate points

b. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
c.

x	-5	-1	9	8	-1
y	1	7	23	17	1

d.
diagram of a relation between two sets

Explanation:

To determine which represents a function, we use the definition of a function: each input (x - value) must have exactly one output (y - value).

Step 1: Analyze Option A

In the graph of Option A, we check the x - coordinates of the points. Let's list the points: Let's assume the points are \((-3, -2)\), \((-1, 1)\), \((0, -5)\), \((1, 4)\). Each x - value (\(-3\), \(-1\), \(0\), \(1\)) is unique. So, for each x, there is only one y.

Step 2: Analyze Option B

The set of ordered pairs is \(\{(0,1),(3,2),(-8,3),(-7,2),(3,4)\}\). Here, the x - value \(3\) is paired with \(2\) and \(4\). Since one x - value has two different y - values, this is not a function.

Step 3: Analyze Option C

In the table for Option C, the x - value \(-1\) is paired with \(7\) and \(1\). Since one x - value has two different y - values, this is not a function.

Step 4: Analyze Option D

In the mapping diagram of Option D, we look at the inputs (left oval) and their outputs (right oval). The input \(9\) and \(13\) and \(-7\) seem to have multiple outputs (we can see that some inputs are connected to more than one output). So, this is not a function.

Answer:

A