To check if a function is linear, one of the criteria is that the ratio of the difference between consecutive y-values to the difference between their corresponding x-values remains constant, i.e., (y2 - y1)/(x2 - x1) = (y3 - y2)/(x3 - x2), and so on.
Let's follow the steps to find out whether or not the function is linear:
Step 1: Check the differences between consecutive f(x) values [y-values] and its domain values [x-values].
- The given x-values are 1, 2, and 4, and the differences between them are (2 - 1) = 1 and (4 - 2) = 2.
- The given y-values are 5, 6, and 7, and the differences between them are (6 - 5) = 1 and (7 - 6) = 1.
Step 2: Calculate the ratio of differences of above y-values and x-values.
- The ratios of differences are 1/1 = 1 and 1/2 = 0.5
Here, we see that the ratio of the differences isn't the same in both cases. Hence, the function f isn't linear. Therefore, the answer is that f(x) is NOT LINEAR.