What is "the range of which function is (2?

The range of a function is the set of all possible output values (y-values) that the function can produce. When we are told that the range of a function is (2, ∞), it means the following:

• Definition: The range represents all the y-values that the function actually takes on. No y-value outside of this interval is ever produced by the function. See more about Definition%20of%20Range.

• Interval Notation: The expression (2, ∞) is an interval notation. It specifies a set of real numbers.

• Interpretation:

  • "(" means the endpoint is not included. In this case, 2 is not included in the range.
  • "∞" means positive infinity. It indicates that the y-values can increase without bound.

• Therefore: The function produces y-values that are strictly greater than 2, and can be arbitrarily large. So, it means y > 2. Check about Interval%20Notation here.

• Example: A function like f(x) = x² + 2, where x is any real number, has a range of [2, ∞) because the lowest value x² can take is 0, so the lowest output value is 2. However, a slight modification, such as f(x) = e^x + 2 has a range of (2, ∞) because e^x is always strictly greater than 0. So f(x) is strictly greater than 2. Here is more about Function%20Examples.

• Finding the Range: Determining the range of a function often depends on the type of function. Common methods include:

  • Analyzing the graph.
  • Considering the domain.
  • Finding the inverse function.
  • Using calculus (for finding maximum and minimum values). More in this topic Finding%20Range%20Methods.