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

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:

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.

3units/ 5 feet = 60 units/ 100 feet3 units/ 5 feet = 18 units/ 30 feetthe dimensions of the scale drawing are 60 units by 18 units.hope this !

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.