This diagram is a scatter plot which represents a set of data. Data on a scatter plot can fit one of three descriptions: positive (increasing), negative (decreasing) or no association (points do not form any kind of line). Given this data and the line of best fit, or the line that pass through the majority of the points, it is a decreasing line. Since the line goes downhill, it is a negative association.
For a linear function the First Differences of the y-values must be a constant. i.e. if we take the difference between any two consecutive y values or values of f(x) it should be the constant. For this rule to work, x values must change by the same number every time, which is true for all three given functions.
For function f:
The values of f(x) are: 5,8,11,14
We can see the difference in consecutive two values is a constant i.e. 3, so the First Difference is the same. Hence, function f is a linear function.
For function g:
The values of g(x) are: 8,4,16,32
We can see the difference among two consecutive values is not a constant. Since the first differences are not the same, this function is not a linear.
For function h:
The values of h(x) are: 28, 64, 100, 136
We can see the difference among two consecutive values is a constant i.e. 36. Therefore, function h is a linear function.
