Match the function to its domain: NOTE: Enter the letter for the domain in the answer box. Letters may be used more than once. 1. \( f(x)=5-x \) 2. \( f(x)=\frac{x-2}{x+4} \) 3. \( f(x)=\frac{x-2}{x+2}+\frac{x+5}{x-2} \) 4. \( f(x)=\frac{\frac{x}{x-5}}{x+\frac{x}{x+2}} \) A. \( \{x \mid x \) is a real number \( \} \) B. \( \{x \mid x \) is a real number and \( x \neq-2 \) and \( x \neq 2\} \) C. \( \{x \mid x \) is a real number and \( x \neq-4\} \) D. \( \{x \mid x \) is a real number and \( x \neq-2 \) and \( x \neq 5\} \)

1. A 2. C 3. B 4. D The first function \( f(x) = 5 - x \) is a simple linear function, which can take any real number as input—hence its domain is all real numbers. For the second function \( f(x) = \frac{x-2}{x+4} \), the denominator cannot equal zero, so when \( x = -4 \), it’s undefined. The third function \( f(x) = \frac{x-2}{x+2}+\frac{x+5}{x-2} \) has restrictions where \( x \) cannot be 2 and -2 as those values would make the denominators zero. Finally, the fourth function has restrictions where \( x \) cannot be 5 and -2 as they would similarly make the denominator zero.