Which function family are these 3? thanks..

1) Function; Linear Function (y=x)

2) Function; Exponential Function (y=bˣ)

3) Not a function.

Step-by-step explanation:

So, let's go through each table of values. I'm also going to graph them (see attached graphs) because it will make things simpler and provide a visual.

First, also recall what the definition of a function is. A function is a function if and only if an x only has one distinct y-value. No x can have two or more y-values. For instance, (1,2) and (1,3) is not a function between the x repeats. So, let's go through the choices:

1)

We have the table as shown. Let's plot the points. See TABLE 1:

First, there are no repeating x-values, so we can be sure that this is indeed a function.

Looking at the graph, we can see that this resembles a linear graph. So, the parent function of this is a line.

The parent function of a line is:

So, table 1 is associated with a linear function.

2)

Let's again plot the points. See TABLE 2.

Again, there are no repeating x-values, so this is also a function.

Looking at the graph, this resembles an exponential function. The function increases slowly at first but starts increasing increasingly fast. The parent function is thus an exponential function.

So, table 2 is associated with an exponential function.

3)

First, notice how all the x-coordinates are repeating. And since they do not equal the same thing, this is not a function.

Table 3 is not a function and so has no corresponding family function.

Note that a function has one x-value assigned to one y-value. If an x-value has more then one y-value then it is not a function.

Question 1:

No x value is given more then y value so this is a function.

If we plot the points, it goes up in a steady line. Thus, this makes it a linear function since it has one slope.

Question  2:

No x value is given more then y value so this is a function.

If we plot the points, it starts going up at a slow pace. After a while, the points go up at a fast pace making it where it doesn't have one slope. Since its a curve like function, it is exponential.

Question 3:

All x values are the same but with different y-values. Thus, makes this not a funtion.

Best of Luck!

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9