Question

Determine the relationship described in each table.

Answer 1

Table 1: The difference between consecutive x values is 1.

But there is no relation between the y- values. The difference as well as the ratio between consecutive y values is not same. Plotting these values on a graph gives an exponential function.

Table 2: The difference between consecutive x values is 1. The difference between consecutive y values is 4. The slope of the function is 4. Hence, it is a linear equation.

Table 3: The difference between the x values is 1.

The difference and the ratio between the consecutive y values is not same. While we plot the points, the graph comes as quadratic.

Table 4: The ratio between the consecutive y values is constant i.e 2.

Hence, this is an exponential equation.

Answer 2

For the first table, the y-values are not equally spaced and the ratios of y are not the same, but by plotting them and observing the graph that results, it looks like the points lie on an exponential curve. The second table is linear because when x changes by 1, y changes by 4. The third table is a quadratic model because even if the first differences of y are not the same, the second differences of y have the same value of 8. The fourth table is exponential because the ratio of y-values is 2, which is the same between each set of numbers.