Answer:
No, it is not a linear function.
Explanation:
If you look at the change in the x-values, you'll see that it increases by 1 each time. But, if you look at the y-values, you'll see that they don't change by the same increment as it goes from 4 to 9 (which means it increased by 5) and from 9 to 16 (which means it increased by 7). For it to be considered a linear function, the change in the y-value has to be the same every time for each increment in the x-value.
If you're ever in doubt, just graph the points on a piece of paper and see if they form a straight line. If they do, then it is a linear function. If they don't then its not linear.
Hope this helps!