Which of the function rules below would result in the following table of values? input: 2 4 6 10 output: 5 9 13 21 a. output = input + 3 b. output = 3*input - 1 c. output = 2 * input + 1d. output = input + 5

Choice C) Output = 2*Input + 1

Let's go through the choices one by one. The idea is that we replace each "input" with the number given in the table, and it should correspond to the proper output value in the same given table.

Choice A says we add 3 to the input, so if the input is 2, then input+3 = 2+3 = 5 is the output. This matches with the first output shown. However, if the input is 4, then input+3 = 4+3 = 7 and it doesn't match with the second output 9.

So choice A is crossed off the list.

Choice B)

Replace "input" with 2, which is the first input value listed

Output = 3*Input - 1

Output = 3*2 - 1

Output = 6 - 1

Output = 5

This matches with the first output

Now replace "input" with 4 and repeat the same steps above

Output = 3*Input - 1

Output = 3*4 - 1

Output = 12 - 1

Output = 11

This doesn't match with the 9 shown as the second output. Cross choice B off the list.

Choice C)

Plug in input = 2

Output = 2*Input + 1

Output = 2*2 + 1 replace 'input' with 2

Output = 4 + 1

Output = 5 ... works

Repeat for input = 4

Output = 2*Input + 1

Output = 2*4 + 1

Output = 8 + 1

Output = 9 ... works

Repeat for input = 6

Output = 2*Input + 1

Output = 2*6 + 1

Output = 12 + 1

Output = 13 ... works

Repeat for input = 10

Output = 2*Input + 1

Output = 2*10 + 1

Output = 20 + 1

Output = 21 ... works

Each input produces the proper output as shown in the given table. So that's why choice C is the answer

Choice D)

Output = Input + 5

Output = 2 + 5

Output = 7

The input 2 leads to the output 7, but the table shows 5 as the output we want. So choice D is crossed off the list.

the first one, all those points on the line just make a strait line.