How to Find the Range of a Function

Oct 13, 2025 by miodeya.com 129 views

**Find the Range of a Function: A Comprehensive Guide** =====================================================

What is the Range of a Function?

The range of a function is the set of all possible output values it can produce for the given input values. In other words, it is the set of all possible y-values that the function can take. The range is an essential concept in mathematics, particularly in algebra and calculus.

How to Find the Range of a Function

To find the range of a function, you need to determine the set of all possible output values. Here are the steps to follow:

Step 1: Identify the Function

The first step is to identify the function for which you want to find the range. In this case, we are given a table of values for the function.

Step 2: Examine the Table of Values

Examine the table of values to identify the minimum and maximum y-values. The minimum y-value is the smallest value in the table, while the maximum y-value is the largest value.

Step 3: Determine the Range

The range of the function is the set of all possible y-values between the minimum and maximum y-values. If there are any gaps or holes in the table, you need to consider them when determining the range.

Example: Finding the Range of a Function

Let's consider the function defined by the table below:

x	1	-7	-4	2	0	-1
y	9	-2	-8	5	1	9

To find the range of this function, we need to examine the table of values.

Step 1: Identify the Minimum and Maximum y-Values

The minimum y-value is -8, and the maximum y-value is 9.

Step 2: Determine the Range

The range of the function is the set of all possible y-values between -8 and 9, inclusive.

Q&A: Finding the Range of a Function

Q: What is the range of a function?

A: The range of a function is the set of all possible output values it can produce for the given input values.

Q: How do I find the range of a function?

A: To find the range of a function, you need to examine the table of values to identify the minimum and maximum y-values, and then determine the set of all possible y-values between them.

Q: What if there are gaps or holes in the table?

A: If there are gaps or holes in the table, you need to consider them when determining the range.

Q: Can the range of a function be a single value?

A: Yes, the range of a function can be a single value if the function is a constant function.

Q: Can the range of a function be an interval?

A: Yes, the range of a function can be an interval if the function is a linear function.

Q: Can the range of a function be a set of discrete values?

A: Yes, the range of a function can be a set of discrete values if the function is a step function.

Conclusion

In conclusion, finding the range of a function is an essential concept in mathematics. By following the steps outlined in this article, you can determine the range of a function and understand its behavior. Remember to examine the table of values, identify the minimum and maximum y-values, and determine the set of all possible y-values between them.

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