Analyze the domain and range of each rational function. Then compare the similarities and differences.

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Domain and Range of f(x): Domain: The function f(x) = (x + 5) / (x - 2) is undefined when the denominator is zero. Therefore, x ≠ 2. The domain is all real numbers except x = 2. Range: The range is all real numbers except the horizontal asymptote, which occurs at y = 1 (as x approaches infinity, f(x) approaches 1). Domain and Range of g(x): Domain: The function g(x) = (x + 3) / (x + 1) is undefined when the denominator is zero. Therefore, x ≠ -1. The domain is all real numbers except x = -1. Range: The range is all real numbers except the horizontal asymptote, which occurs at y = 1 (as x approaches infinity, g(x) approaches 1). Similarities and Differences: Both functions have a horizontal asymptote at y = 1. Both functions have a vertical asymptote where the denominator is zero (x = 2 for f(x) and x = -1 for g(x)). The domain and range restrictions are similar, but occur at different x-values due to the different vertical asymptotes.

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Analyze the domain and range of each rational function. Then compare the similarities and differences.

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