graph the function. Find the zeros of each function and the x- and y-intercepts
of each graph, if any exist. From the graph, determine the domain and range of each function, list
the intervals on which the function is increasing, decreasing or constant, and find the relative and
absolute extrema, if they exist. f(x) = |2 − x| / 2 − x

Here is the graph of the function \( f(x) = \frac{|2 - x|}{2 - x} \). It shows the following:

- The function is **constant** and equals 1 for \( x < 2 \).
- The function is **constant** and equals -1 for \( x > 2 \).
- There is a **discontinuity** at \( x = 2 \), where the function is undefined.

### Summary:
1. **Zeros**: None.
2. **X-intercept**: None.
3. **Y-intercept**: \( (0, 1) \).
4. **Domain**: \( (-\infty, 2) \cup (2, \infty) \).
5. **Range**: \( \{-1, 1\} \).
6. **Increasing/Decreasing Intervals**: Constant on both \( (-\infty, 2) \) and \( (2, \infty) \).
7. **Extrema**: None (no relative or absolute maxima/minima).

Would you like further details or clarifications?

### Related questions:
1. How can you interpret the jump at \( x = 2 \) mathematically?
2. What happens if we modify the denominator slightly, such as \( 2 - 2x \)?
3. How would this function behave with different absolute values in the numerator?
4. What is the difference between a removable and a non-removable discontinuity?
5. How does this function compare to a step function?

**Tip**: Discontinuities like this one are called "jump discontinuities," where the function value jumps between two different levels.

Graph the function. Find the zeros of each function and the x- and y-intercepts of each graph, if any exist. From the graph, determine the domain and range of each function, list the intervals on which the function is increasing, decreasing or constant, and find the relative and absolute extrema, if they exist. f(x) = |2 − x| / 2 − x

Explore the detailed graph analysis of the function f(x) = |2 − x| / (2 − x). Learn how to find the domain, range, and intercepts of the function, identify intervals of increase and decrease, and understand the nature of its discontinuities. Suitable for students in Grades 10-12.

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