which of the following represent the range of the function f(x)=-4x+1 for the domain

To find the range of the function f(x) = -4x + 1, we need to determine the set of all possible values that the function can output for different input values.

The domain of a linear function like f(x) = -4x + 1 is typically considered to be all real numbers, unless there are any specific restrictions mentioned in your question.

To find the range, we can either graph the function or analyze its behavior.

1. Graph Method:
- Graph the function f(x) = -4x + 1 on a coordinate plane.
- Identify the vertical extent of the graph, which represents the range of the function.
- The range can be determined by considering the lowest and highest points on the graph.

2. Analytical Method:
- Since f(x) = -4x + 1 is a linear function, it has a constant slope of -4.
- As the input values (x) change, the output values (f(x)) change in a predictable manner.
- In this case, as x increases, f(x) decreases because of the negative slope.
- Therefore, the range of this function is all real numbers because there are no limitations on how high or low f(x) can go.

In conclusion, the range of the function f(x) = -4x + 1 for the given domain is all real numbers.