Find domain and range
- x - 2y = 4
Answer (1)
The equation -x - 2y = 4 represents a straight line. Let's find its domain and range.Step 1: Solve for yTo better understand the domain and range, let's solve the equation for y:[tex]$\sf{-2y = x + 4}$[/tex][tex]$\sf{y = (-\frac{1}{2})x - 2}$[/tex]Step 2: Determine the DomainThe domain of a function is the set of all possible x-values. Since this is a linear equation (a straight line), there are no restrictions on the x-values. x can be any real number.Therefore, the domain is: (-∞, ∞) or all real numbers.Step 3: Determine the RangeThe range of a function is the set of all possible y-values. Because this is a linear equation representing a line with a non-zero slope, the y-values also extend infinitely in both directions.Therefore, the range is: (-∞, ∞) or all real numbers.Final answer:Domain: (-∞, ∞)Range: (-∞, ∞)
