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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

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.
The range of the function is made up of all real numbers, but the domain of the function is not. - no response given

The domain of the function is made up of all real numbers, but the range of the function is not.

1 answer

To analyze the function \( f(t) = 4t + 95 \):

  1. Domain: The domain of this linear function consists of all real numbers. There are no restrictions on the value of \( t \) (you can input any real number).

  2. Range: Since \( f(t) \) is a linear function with a slope of 4 (which is a non-zero constant), it can produce any real value as output. As \( t \) increases or decreases without bounds, \( f(t) \) also increases or decreases without bounds. Therefore, the range is also all real numbers.

Based on the analysis, the true statement is:

The domain and range of the function are both made up of all real numbers.