Question

2. 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

Solution:

The Ordered pair of the function is

x :  0      1     2   3     4   5

y:   13  21  29  37  45   53  

(a)  $\frac{\text{Change in y values}}{\text{Change in x values}}=\frac{21-13}{1-0}=\frac{29-21}{2-1}=\frac{37-29}{3-2}=\frac{45-37}{4-3}=\frac{53-45}{5-4}=8$

Slope between two points are same.So,the function Represented in terms of ordered pairs Linear.

(b) As, you can each Successor of x values is obtained by adding 1 to it's Predecessor.

and , each Successor of y values is obtained by adding 8 to it's Predecessor.

(c) Taking any two ordered pairs , (0,13) and (1,21) we can find an equation of line passing through these 5 points (2,29),(3,37),(4,45),(5,53)

Equation of line passing through passing through two points $(x_{1},y_{1}),{\text and} (x_{2},y_{2})$ is given by

 = $\frac{y-y_{1}}{x-x_{1}}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

= $\frac{y-13}{x-0}=\frac{21-13}{1-0}$

→ y -13 = 8 x

→ y = 8 x + 13

So, Y intercept = 13