f refers to function with domain [0,1] and range (0, 1]. Sketch the graphs of the indicated functions and specify their domains and ranges f(x+2)

The function \( f(x+2) \) represents a horizontal shift of the original function \( f(x) \) by 2 units to the left. 

### Domain and Range of \( f(x+2) \):
1. **Domain**: Since \( f(x) \) is defined on the domain \([0,1]\), shifting it by 2 units to the left results in a new domain \([-2, -1]\). Thus, the domain of \( f(x+2) \) is:
   \[
   \text{Domain: } [-2, -1]
   \]

2. **Range**: The range of \( f(x+2) \) will remain the same as that of \( f(x) \), because a horizontal shift does not affect the range. Thus, the range is:
   \[
   \text{Range: } (0, 1]
   \]

### Graph Sketch:
To sketch \( f(x+2) \), take the graph of \( f(x) \), which lies in the interval \([0,1]\) and has a range in \((0, 1]\), and shift it left by 2 units. The resulting graph will now be plotted over the domain \([-2, -1]\), while keeping the same range \((0, 1]\).

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### Would you like me to provide a graphical sketch of the function?

### Related Questions:
1. How does a vertical shift affect the domain and range of a function?
2. What happens if you apply a horizontal stretch or compression to \( f(x) \)?
3. How would the function \( f(x-2) \) behave in terms of domain and range?
4. What are the effects of reflecting a function about the y-axis?
5. How would you define a piecewise function with a restricted domain and range?

#### Tip: Horizontal transformations affect the x-values (domain) while keeping the y-values (range) the same.

f refers to function with domain [0,1] and range (0, 1]. Sketch the graphs of the indicated functions and specify their domains and ranges f(x+2).

Explore how to sketch the graph of the function f(x+2) when the original function has a domain of [0,1] and a range of (0,1]. This example demonstrates the effect of horizontal shifts on the domain and range. Suitable for students in Grades 10-12.

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