Question

This table shows the input and output of a function.

(A) write an equation, in function notation that would fit the inputs and outputs of the table. show your work that proves your equation for the table

input output
3 5
4 7
6 11
11 21

Answer 1

We are given table of input and output:

input output

3 5

4 7

6 11

11 21

We take x coordinate as input values and y-coordinates as output.

So, we can take two two coordinates from the given table (3,5) and (4,7).

Now, we need to find the slope between those two coordinates:

`\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(3,\:5\right),\:\left(x_2,\:y_2\right)=\left(4,\:7\right)`

`m=(7-5)/(4-3)`

`m=2`

Now, applying point slope formula

y-y1 = m(x-x1)

y - 5 = 2(x-3)

y -5 = 2x -6

Adding 5 on both sides, we get

y -5+5 = 2x -6+5

y = 2x -1.

Therefore, required eqution is y=2x-1.

In order to prove the equation for the table, we can plug x=3,4,6 and 11 in the euqation.

y=2(3)-1 = 6 -1 = 5

y =2(4) -1 = 8 - 1 = 7

y =2(6) - 1 = 12 -1 = 11.

y = 2(11) - 1 = 22-1 = 21.

Each input in table gives same vaule of output given in the table.