Answer:
First table models Linear, second quadratic and third one exponential functions.
Step-by-step explanation:
To find whether the given table models a linear function there should be a constant change in y values with the constant change in x values of the table.
We take the example of first table written as linear.
Here change in x values is
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
Similarly change in y values is
1 - 4 = -3
-2 - 1 = -3
-5 -(-2) = -3
There is a common difference in y values = -3
So the given table models linear function.
We take the second table.
For quadratic function with the constant change in x values, difference of difference in y values is constant.
Change in x - values
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
Difference in y values
1 - 0 = 1
4 - 1 = 3
9 - 4 = 5
Now difference in difference of y values
3 - 1 = 2
5 - 3 = 2
Here, difference in difference of y values is 2
So the given table models a quadratic equation.
Now we take the third table.
For exponential function in the form of [tex]f(x) = a(r)^{n}[/tex] there should be a common ratio in the terms of y values.
[tex]\frac{\text{Second term of y}}{\text{First term of y }}= \frac{2}{1}=2[/tex]
[tex]\frac{\text{Third term of y}}{\text{Second term of y }}= \frac{4}{2}=2[/tex]
So there is a common ratio of 2 in each term.
Therefore, the given table models exponential equation.
First table models Linear, second quadratic and third one exponential functions.
