Question
A) Rajendra writes the equation f(t) = 4t + 95 to represent a function. Which statement is true?
(1 point)
The domain and range of the function are both made up of all real numbers.
The range of the function is made up of all real numbers, but the domain of the function is not.
Neither the domain nor the range of the function is made up of all real numbers.
The domain of the function is made up of all real numbers, but the range of the function is not.
(1 point)
The domain and range of the function are both made up of all real numbers.
The range of the function is made up of all real numbers, but the domain of the function is not.
Neither the domain nor the range of the function is made up of all real numbers.
The domain of the function is made up of all real numbers, but the range of the function is not.
Answers
GPT-4o mini
To analyze the function \( f(t) = 4t + 95 \):
1. **Domain**: The variable \( t \) can take any real number value. Therefore, the domain of the function is all real numbers.
2. **Range**: Since \( f(t) \) is a linear function with a slope of 4 (which is not zero), as \( t \) takes all real number values, \( f(t) \) will also take all real number values. For very large or small values of \( t \), \( f(t) \) will correspondingly be very large or very small. Thus, the range of the function is also all real numbers.
Based on this analysis, the correct statement is:
**The domain and range of the function are both made up of all real numbers.**
1. **Domain**: The variable \( t \) can take any real number value. Therefore, the domain of the function is all real numbers.
2. **Range**: Since \( f(t) \) is a linear function with a slope of 4 (which is not zero), as \( t \) takes all real number values, \( f(t) \) will also take all real number values. For very large or small values of \( t \), \( f(t) \) will correspondingly be very large or very small. Thus, the range of the function is also all real numbers.
Based on this analysis, the correct statement is:
**The domain and range of the function are both made up of all real numbers.**