Question

write the range of the function in interval notation. f(x)=3 - x a. (-∞, ∞) b. (3, ∞) c. (-∞, -3) d. the range does not exist.

Explanation:

Step1: Identify the function type

The function \( f(x) = 3 - x \) is a linear function (in the form \( y = mx + b \), where \( m=-1 \) and \( b = 3 \)).

Step2: Analyze the range of a linear function

For a linear function with a non - zero slope (here \( m=-1
eq0 \)), the graph is a straight line that extends infinitely in both the positive and negative \( y \) - direction. This means that the set of all possible output values (the range) includes all real numbers. In interval notation, the set of all real numbers is represented as \( (-\infty,\infty) \).

Answer:

A. \((-\infty, \infty)\)