Input Output Functions
In input and output functions technique while we have a number of normal methods
, we have to exchange some meaning in the known normal method, and in result we will obtain different extra values. In this, the distinctive method is known as regulation and the value we are return with this input value and the meaning we are getting after replacement and get the product, that result is known as output. We use bulk of substitution in input and output in value rule.
Input Output Function Example Problem 1:
Find the missing number in input and output function table.
x(input)
y(output)
?
-2
3
1
6
4
8
6
4
?
Solution:
Note down these as prearranged pairs (points) and choose any two to place the slope and after you have the slope utilize
the point-slope formula of a line:
(?, -2), (3, 1), (6, 4), (8 , 6), (4, ?).
Use (3, 1), (6,4) to obtain the slope:
The formula used to locate the slope of the two points slope of a line is
m = '(y_(2) - y_(1)) / (x_(2) - x_(1))'
Here x1 = 3, x2 = 6, y1 = 1 and y2 = 4
By substituting all the values into the formula we can obtain the slope of the line
(4 - 1)/ (6 - 3) = 3 / 3
Slope m = 1
Use any point in the point-slope formula y-y1 = m(x-x1):
y - 1 = 1(x - 3)
= x - 3
y 1 + 1 = x - 3 +1 (adding 1 on both sides)
y = x - 2 this is the condition for the given input output functional table.
By this condition we can get the value for the remaining number
Now to find (?, -2) we recognize that y is -2, by replacing the value into the equation above:
y = x - 2
-2 = 1(x) 2 (adding 2 on both sides)
-2 + 2 = x 2 + 2
0 = x
x = 0, the obtained ordered pair is (0, -2).
To obtain the value for (4, ?) we recognize that x is 4 by replacing the value into the equation ,
We get, y = x - 2
y = 4 - 2
y = 2
The obtained ordered pair is (4, 2).
Input Output Function Example Problem 2:
Obtain the condition for the missing number in the input output function table,
x(input)
y(output)
10
?
5
0
7
10
?
-25
4
-
Solution:
Note down these as ordered pairs (points) and choose any two points to establish the slope and while you have the slope occupy the point-slope formula of a line:
(10, ?),(5, 0),(7, 10),(?, -25),(4, -5).
Employ (5, 0), (4, -5) to obtain the slope:
The procedure used to obtain the slope of the two points slope of a line is
m = [(y_(2) - y_(1)) / (x_(2) - x_(1))]
Here x1 = 5, x2 = 4, y1 = 0 and y2 = -5
By substituting every value into the formula we can obtain the slope of the line
(-5 - 0) / (4 - 5)
= - 5 / -1
Slope m = 5
Employ any two points in the point-slope formula y-y1 = m(x-x1):
y - 0 = 5(x 5)
y - 0 = 5x - 25
y = 5x - 25 this is the condition for the given input output function table.
By using this condition we can obtain the value for missing number in function table.
For (10, ?) we categorize that x is 10, by replacing the value into the conditional equation above we can find the value for y:
y = 5(10) - 25
y = 50 - 25
y = 25, the ordered pair is (10, 25).
For (?, -25) we categorize that y is -25 by replacing the value into the obtained condition equation above,
y = 5x 25
- 25 = 5(x) 25
-25 = 5x 25 (Add 25 on both sides)
-25 + 25 = 5x 25 + 25
0 = 5x
x = 0.
The ordered pair for the obtained condition is (0, 25).
by: johnharmer
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