Question
Rajendra writes the equation f(t)=4t+95
to represent a function. Which statement is true?(1 point)
Responses
The domain and range of the function are both made up of all real numbers.
The domain and range of the function are both made up of all real numbers. - no response given
The domain of the function is made up of all real numbers, but the range of the function is not.
The domain of the function is made up of all real numbers, but the range of the function is not. - incorrect
Neither the domain nor the range of the function is made up of all real numbers.
Neither the domain nor the range of the function is made up of all real numbers. - no response given
The range of the function is made up of all real numbers, but the domain of the function is not.
to represent a function. Which statement is true?(1 point)
Responses
The domain and range of the function are both made up of all real numbers.
The domain and range of the function are both made up of all real numbers. - no response given
The domain of the function is made up of all real numbers, but the range of the function is not.
The domain of the function is made up of all real numbers, but the range of the function is not. - incorrect
Neither the domain nor the range of the function is made up of all real numbers.
Neither the domain nor the range of the function is made up of all real numbers. - no response given
The range of the function is made up of all real numbers, but the domain of the function is not.
Answers
GPT-4o mini
The function \( f(t) = 4t + 95 \) is a linear function, where \( t \) represents the independent variable.
1. **Domain**: The domain of this function (the values that \( t \) can take) is all real numbers, as there are no restrictions on \( t \).
2. **Range**: The range of this function (the possible values of \( f(t) \)) is also all real numbers. As \( t \) takes on all real values, \( 4t + 95 \) can produce any real number. Specifically, as \( t \) approaches negative infinity, \( f(t) \) approaches negative infinity, and as \( t \) approaches positive infinity, \( f(t) \) approaches positive infinity.
Therefore, the true statement is:
**The domain and range of the function are both made up of all real numbers.**
1. **Domain**: The domain of this function (the values that \( t \) can take) is all real numbers, as there are no restrictions on \( t \).
2. **Range**: The range of this function (the possible values of \( f(t) \)) is also all real numbers. As \( t \) takes on all real values, \( 4t + 95 \) can produce any real number. Specifically, as \( t \) approaches negative infinity, \( f(t) \) approaches negative infinity, and as \( t \) approaches positive infinity, \( f(t) \) approaches positive infinity.
Therefore, the true statement is:
**The domain and range of the function are both made up of all real numbers.**