Find the DOMAIN and RANGE of th 15. $$ y=2 x-1 $$ $$ y=\sqrt{x-7} $$

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UpStudy AI · Accepted Answer

Sure! Let's determine the **domain** and **range** for each of the given functions.

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### 1. $$ y = 2x - 1 $$

**Domain**: The domain of a linear function is all real numbers since there are no restrictions on the value of $$ x $$.

$$
\text{Domain}: \quad (-\infty, \infty)
$$

**Range**: Similarly, the range of a linear function is all real numbers because $$ y $$ can take any real value.

$$
\text{Range}: \quad (-\infty, \infty)
$$

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### 2. $$ y = \sqrt{x - 7} $$

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

$$
x - 7 \geq 0 \quad \Rightarrow \quad x \geq 7
$$

$$
\text{Domain}: \quad [7, \infty)
$$

**Range**: The square root function outputs values that are greater than or equal to zero.

$$
\text{Range}: \quad [0, \infty)
$$

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**Summary:**

1. **$$ y = 2x - 1 $$**
   - **Domain:** $$ (-\infty, \infty) $$
   - **Range:** $$ (-\infty, \infty) $$

2. **$$ y = \sqrt{x - 7} $$**
   - **Domain:** $$ [7, \infty) $$
   - **Range:** $$ [0, \infty) $$

If you have any more questions or need further explanations, feel free to ask!
**Domain and Range:** 1. **$$ y = 2x - 1 $$** - **Domain:** All real numbers ($$ -\infty $$ to $$ \infty $$) - **Range:** All real numbers ($$ -\infty $$ to $$ \infty $$) 2. **$$ y = \sqrt{x - 7} $$** - **Domain:** $$ x \geq 7 $$ ($$ [7, \infty) $$) - **Range:** $$ y \geq 0 $$ ($$ [0, \infty) $$)

Find the DOMAIN and RANGE of th 15. \( y=2 x-1 \) \( y=\sqrt{x-7} \)

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