The domain of a function is the set of positive integers less than 12. If `y=f(x)=|x-4|`, find all ordered pairs satisfying the function. Graph the function.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the Domain
The domain of the function is given as the set of positive integers less than 12. Therefore, the domain is:
\[ \text{Domain} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} \]

### Step 2: Define the Function
The function is defined as:
\[ y = f(x) = |x - 4| \]

### Step 3: Calculate the Function Values
We will calculate the value of \( f(x) \) for each integer in the domain.

- For \( x = 1 \):
\[ f(1) = |1 - 4| = | -3 | = 3 \]

- For \( x = 2 \):
\[ f(2) = |2 - 4| = | -2 | = 2 \]

- For \( x = 3 \):
\[ f(3) = |3 - 4| = | -1 | = 1 \]

- For \( x = 4 \):
\[ f(4) = |4 - 4| = |0| = 0 \]

- For \( x = 5 \):
\[ f(5) = |5 - 4| = |1| = 1 \]

- For \( x = 6 \):
\[ f(6) = |6 - 4| = |2| = 2 \]

- For \( x = 7 \):
\[ f(7) = |7 - 4| = |3| = 3 \]

- For \( x = 8 \):
\[ f(8) = |8 - 4| = |4| = 4 \]

- For \( x = 9 \):
\[ f(9) = |9 - 4| = |5| = 5 \]

- For \( x = 10 \):
\[ f(10) = |10 - 4| = |6| = 6 \]

- For \( x = 11 \):
\[ f(11) = |11 - 4| = |7| = 7 \]

### Step 4: List the Ordered Pairs
Now we can list the ordered pairs \((x, f(x))\):
- \( (1, 3) \)
- \( (2, 2) \)
- \( (3, 1) \)
- \( (4, 0) \)
- \( (5, 1) \)
- \( (6, 2) \)
- \( (7, 3) \)
- \( (8, 4) \)
- \( (9, 5) \)
- \( (10, 6) \)
- \( (11, 7) \)

### Step 5: Graph the Function
To graph the function, plot the points from the ordered pairs on a Cartesian plane. The x-axis will represent the values of \( x \) (from 1 to 11), and the y-axis will represent the values of \( f(x) \).

### Summary of Results
The ordered pairs satisfying the function are:
\[ (1, 3), (2, 2), (3, 1), (4, 0), (5, 1), (6, 2), (7, 3), (8, 4), (9, 5), (10, 6), (11, 7) \]