Question

what are the domain and range of $f(x) = -37$?

a domain: all real numbers greater than or equal to $-37$
range: all real numbers

b domain: $\\{ -37 \\}$
range: all real numbers

c domain: all real numbers
range: all real numbers greater than or equal to $-37$

d domain: all real numbers
range: $\\{ -37 \\}$

Explanation:

Step1: Analyze the function type

The function \( f(x) = -37 \) is a constant function. A constant function has the same output (value) for every input \( x \).

Step2: Determine the domain

For a constant function, there are no restrictions on the input \( x \). \( x \) can be any real number because we can plug in any real number for \( x \) and the function will still output \( -37 \). So the domain is all real numbers.

Step3: Determine the range

Since the function outputs \( -37 \) for every input \( x \), the only value in the range is \( -37 \). So the range is the set containing only \( -37 \), which is \( \{ -37 \} \).

Answer:

D. Domain: All real numbers
Range: \( \{ -37 \} \)