What is the Range of a Function? | Simple Explanation for Class 10

S6-SA1-0321

What is the Range of a Function (basic intro)?

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

The Range of a function is the set of all possible output values that the function can produce. Think of it as all the answers you can get when you put different valid inputs into the function.

Simple Example

Quick Example

Imagine a mobile recharge shop where you can recharge for Rs 10, Rs 20, Rs 50, or Rs 100. If the shop owner only offers these specific recharge amounts, then these amounts (10, 20, 50, 100) form the Range of the 'recharge amount' function.

Worked Example

Step-by-Step

Let's find the Range for the function f(x) = x + 5, if the allowed input values (Domain) for x are {1, 2, 3}. --- Step 1: Take the first input value, x = 1. Calculate f(1) = 1 + 5 = 6. --- Step 2: Take the second input value, x = 2. Calculate f(2) = 2 + 5 = 7. --- Step 3: Take the third input value, x = 3. Calculate f(3) = 3 + 5 = 8. --- Step 4: Collect all the output values we found. These are {6, 7, 8}. --- Answer: The Range of the function f(x) = x + 5 for the given Domain is {6, 7, 8}.

Why It Matters

Understanding the Range helps scientists and engineers know what outcomes are possible. In AI/ML, it helps predict the limits of a model's output. Doctors use it to understand the possible range of a patient's vital signs, while engineers use it to design systems that operate within safe limits.

Common Mistakes

MISTAKE: Confusing Range with Domain. | CORRECTION: Domain is the set of all possible INPUT values, while Range is the set of all possible OUTPUT values.

MISTAKE: Forgetting to list all possible outputs, especially if inputs are limited. | CORRECTION: Always calculate the output for EACH valid input value in the Domain to ensure no output is missed.

MISTAKE: Thinking the Range is always the same as the Domain. | CORRECTION: The Range can be different from the Domain, often a subset of it, or even contain completely different types of values.

Practice Questions

Try It Yourself

QUESTION: What is the Range of the function f(x) = 2x, if the Domain for x is {0, 1, 2}? | ANSWER: {0, 2, 4}

QUESTION: A function g(x) gives the square of x. If the Domain is {-2, -1, 0, 1, 2}, what is the Range of g(x)? | ANSWER: {0, 1, 4}

QUESTION: A small samosa shop sells samosas for Rs 10 each. The number of samosas a customer can buy is 1, 2, 3, 4, or 5. If f(x) represents the total cost for x samosas, what is the Range of f(x)? | ANSWER: {10, 20, 30, 40, 50}

MCQ

Quick Quiz

For the function h(x) = x - 3, if the Domain is {5, 7, 9}, what is the Range?

{5, 7, 9}

{2, 4, 6}

{-2, -4, -6}

{3, 5, 7}

The Correct Answer Is:

When x=5, h(5)=5-3=2. When x=7, h(7)=7-3=4. When x=9, h(9)=9-3=6. So, the Range is {2, 4, 6}.

Real World Connection

In the Real World

When you use a weather app, it might show you the 'range' of temperatures expected for the day (e.g., 25°C to 35°C). This is like the Range of the temperature function. In cricket, data analysts look at the range of runs scored by a batsman in recent matches to understand their typical performance.

Key Vocabulary

Key Terms

FUNCTION: A rule that assigns each input exactly one output | DOMAIN: The set of all possible input values for a function | OUTPUT: The result obtained after applying the function rule to an input | SET: A collection of distinct objects or numbers

What's Next

What to Learn Next

Great job learning about the Range! Next, you can explore 'Types of Functions' like linear, quadratic, or exponential functions. Understanding the Range will help you predict their behavior and graph them more accurately.