1. **Problem:** Use set notation to specify the domain and range of each relation. 2. **Relation a:** $5x + 2y = 2$ - This is a linear equation representing a line. - The domain of a line is all real numbers because $x$ can be any real number. - The range is also all real numbers because $y$ can take any real value depending on $x$. **Answer:** - Domain: $\{x \in \mathbb{R}\}$ - Range: $\{y \in \mathbb{R}\}$ 3. **Relation b:** $f(x) = -\frac{1}{x+2}$ - The function is a rational function with a denominator $x+2$. - The domain excludes values that make the denominator zero, so $x \neq -2$. - The range is all real numbers except 0 because the function never equals zero. **Answer:** - Domain: $\{x \in \mathbb{R} \mid x \neq -2\}$ - Range: $\{y \in \mathbb{R} \mid y \neq 0\}$ 4. **Relation c:** $y = 4$ - This is a horizontal line where $y$ is always 4. - The domain is all real numbers because $x$ can be any real number. - The range is the single value 4. **Answer:** - Domain: $\{x \in \mathbb{R}\}$ - Range: $\{4\}$ 5. **Relation d:** $\{(1,6), (4,9), (11,37)\}$ - The domain is the set of all first elements of the ordered pairs. - The range is the set of all second elements of the ordered pairs. **Answer:** - Domain: $\{1,4,11\}$ - Range: $\{6,9,37\}$