I am trying to complete this input/output table. Input 0 output blank, input 3/2 output 17/6, input 11/4 output blank, input 3 output 13/3, input blank output 13/2
Your relation could be linear:
using (3/2 , 17,6) and (3, 13/3)
slope = (17/6 - 13/3)/(3/2 - 3) = (-3/2) / (-3/2) = 1
y - 13/3 = 1(x-3)
3y - 13 = 3x-9
3x - 3y = -4
now plug in the given input as x or the given output as y
e.g input = x = 11/4
3(11/4) - 3y = -4
times 4
33 - 12y = -16
-12y = -49
y = -49/-12 = 49/12
do the remaining one in the same way
your relation could have been quadratic:
let's make (3,13/3) the vertex
then
y = a(x-3)^2 + 13/3
but (3/2 , 17/6) lies on it
17/6 = a(3/2 - 3)^2 + 13/3
17/6 = a(9/4) + 13/3
times 12
34 = 27a + 52
27a = -18
a = -18/27 = 2/3
so it could have been
y = (2/3)(x-3)^2 + 13/3
There could have been an infinite number of possible quadratics, not to mention, we could have made it into a cubic, etc.
Hmmm. In general, you cannot fit a quadratic to 4 points. Only a single cubic, but many of higher degree.
Steve, only 2 points were actually given.
(3/2, 17/6)
(3, 13/3)
The others were
(0, ??)
(11/4, ??)
So I could form a unique linear, but an infinite number of quadratics, cubics, etc that pass through those two points.
Once I have an equation, the missing y values of the other 2 points are then found
Oww. My Bad!
To complete the input/output table, let's analyze the given information:
1. For an input of 0, the output is blank.
2. For an input of 3/2, the output is 17/6.
3. For an input of 11/4, the output is blank.
4. For an input of 3, the output is 13/3.
5. For an unknown input, the output is 13/2.
To find the missing values, we can look for any patterns or relationships among the given inputs and outputs.
The first pattern we can identify is that the outputs seem to involve multiplication and addition of the inputs.
Let's examine the given input/output pairs:
1. Input 0, output blank
2. Input 3/2, output 17/6
If we calculate 17/6 divided by 3/2, we get 17/9, which is a consistent relationship between the inputs and outputs.
Using this pattern, we can apply the same relationship to the missing values:
1. For the missing output when the input is 0, we divide 17/9 by 3/2. The division is calculated as (17/9) / (3/2) = 34/27.
2. For the missing output when the input is 11/4, we divide 17/9 by 3/2. The division is calculated as (17/9) / (3/2) = 34/27.
Therefore, the completed input/output table would look like this:
Input 0, output 34/27
Input 3/2, output 17/6
Input 11/4, output 34/27
Input 3, output 13/3
Input blank, output 13/2