Question

1. The table shows a function.

x 0 1 2 3 5 13 21 29 37 45 53 (a) Is the function linear, exponential, or neither?
(b) What is the pattern that you observe in the table? (for example: adding 5 each time x increases by 1, dividing by 2 each time x increases by 3) If there is no pattern, show that there is no pattern.
(c) What is the y-intercept of the function represented by the table? (be sure to write as an ordered pair)

Answer 1

Answer: a) Linear function

b) adding 8 each time x increases by 1

c) (0,13)

Explanation:

For the given table, the rate of change is constant throughout the table.

The rate of change =
`(change\ in\ y)/(change\ in\ x)=(21-13)/(1-0)=8`

Similarly we can check for every interval, the rate of change remains constant .

Thus, it is a linear function and the pattern we observe here is "adding 8 each time x increases by 1".

We know that the ordered pair of y intercept = (0,y)

In the table at x=0, y=13

hence, the y intercept of the given function is (0,13)