Question 6 Consider the function $$ y=\sqrt{4-x} $$. What are the domain and range of this function? domain: $$ x \leq 4 $$, range: $$ y \geq 0 $$ domain: $$ x \leq 2 $$, range: $$ y \geq 2 $$ domain: $$ x \geq 2 $$, range: $$ y \geq 2 $$ domain: $$ x \geq 4 $$, range: $$ y \geq 0 $$

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To determine the domain and range of the function $$ y = \sqrt{4 - x} $$, let's analyze each part step by step.

### **Domain**

The expression inside the square root must be non-negative because the square root of a negative number is not a real number. Therefore:

$$ 4 - x \geq 0 $$

Solving for $$ x $$:

$$ x \leq 4 $$

So, the **domain** is all real numbers $$ x $$ such that $$ x \leq 4 $$.

### **Range**

The square root function always yields non-negative results because it's defined as the principal (non-negative) root. Therefore:

$$ y = \sqrt{4 - x} \geq 0 $$

So, the **range** is all real numbers $$ y $$ such that $$ y \geq 0 $$.

### **Conclusion**

The correct domain and range are:

- **Domain:** $$ x \leq 4 $$
- **Range:** $$ y \geq 0 $$

**Answer:**  
domain: $$ x \leq 4 $$, range: $$ y \geq 0 $$
The domain is $$ x \leq 4 $$ and the range is $$ y \geq 0 $$.

Question 6
Consider the function .
What are the domain and range of this function?
domain: , range:
domain: , range:
domain: , range:
domain: , range:

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