Question

1. what are the domain and range of the graph of f(x)=24? * 8 points

f. domain: all real numbers greater than or equal to 24; range: all real numbers
g. domain: all real numbers; range: all real numbers greater than or equal to 24
h. domain: all real numbers; range: {24}
j. domain: {24}; range: all real numbers

Explanation:

Step1: Analyze the function type

The function \( f(x) = 24 \) is a constant function. For a constant function, there are no restrictions on the input value \( x \), so we first determine the domain.

Step2: Determine the domain

The domain of a function is the set of all possible input values (x - values). For \( f(x)=24 \), \( x \) can be any real number because there are no conditions or restrictions on what \( x \) can be. So the domain is all real numbers.

Step3: Determine the range

The range of a function is the set of all possible output values (y - values). Since \( f(x) \) always equals 24, regardless of the value of \( x \), the only output value is 24. So the range is the set containing only 24, which is \( \{24\} \).

Step4: Match with the options

Now we check the options:

• Option F: Domain is wrong (should be all real numbers, not just those ≥24), Range is wrong (should be {24}, not all real numbers).
• Option G: Range is wrong (should be {24}, not all real numbers ≥24).
• Option H: Domain is all real numbers and Range is {24}, which matches our analysis.
• Option J: Domain is wrong (should be all real numbers, not {24}), Range is wrong (should be {24}, not all real numbers).

Answer:

H. Domain: All real numbers; Range: {24}