Subjects algebra

Domain Range 9A90D6

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1. **State the problem:** Find the domain and range of a function. Since the function is not specified, let's consider a general approach. 2. **Domain:** The domain of a function is the set of all possible input values ($x$) for which the function is defined. 3. **Range:** The range is the set of all possible output values ($y$) the function can take. 4. **Important rules:** - For functions involving square roots, the expression inside must be $\geq 0$. - For functions with denominators, the denominator cannot be zero. 5. **Example:** Suppose the function is $y=\sqrt{x-2}$. 6. **Find domain:** Set the inside of the square root $\geq 0$: $$x-2 \geq 0$$ $$x \geq 2$$ So, the domain is $[2, \infty)$. 7. **Find range:** Since square root outputs are $\geq 0$, the range is $[0, \infty)$. This is the general method to find domain and range.