Function Analysis Online Practice

Question

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Question
Rajendra writes the equation f(t)=4t+95
to represent a function. Which statement is true?(1 point)
Responses

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.

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.

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.

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.
Remaining Attempts : 3
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Answer 1

To analyze the function \( f(t) = 4t + 95 \), let's look at both the domain and range.

1. Domain: The function is a linear function, which means it is defined for all real numbers. There are no restrictions on \( t \) (e.g., no denominators that could be zero or square roots of negative numbers).

2. Range: Since the function is linear and has a non-zero slope (4), as \( t \) takes on all real numbers, \( f(t) \) will also take on all real values. As \( t \) approaches positive or negative infinity, \( f(t) \) will also approach positive or negative infinity.

Based on this analysis, we can conclude that:

• The domain of the function is made up of all real numbers.
• The range of the function is also made up of all real numbers.

Therefore, the correct statement is:

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