What is Range of an Equation? | Simple Explanation for Class 8

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What is the Range of an Equation?

Grade Level:

Class 8

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The 'Range' of an equation tells us all the possible output values (y-values) we can get when we put different input values (x-values) into the equation. It's like finding the set of all answers the equation can give.

Simple Example

Quick Example

Imagine a mobile recharge shop where the cost (y) for 'x' GB of data is given by the equation y = 10x + 50 (50 is a fixed service charge). If you can buy data packs for 1 GB, 2 GB, or 3 GB, the possible costs (range) would be the amounts you pay for each: Rs 60 (for 1 GB), Rs 70 (for 2 GB), and Rs 80 (for 3 GB).

Worked Example

Step-by-Step

Let's find the Range of the equation y = x + 3, if the input values (x) can be 1, 2, 3, and 4.

Step 1: Substitute the first x-value, x = 1, into the equation.
y = 1 + 3 = 4
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Step 2: Substitute the second x-value, x = 2, into the equation.
y = 2 + 3 = 5
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Step 3: Substitute the third x-value, x = 3, into the equation.
y = 3 + 3 = 6
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Step 4: Substitute the fourth x-value, x = 4, into the equation.
y = 4 + 3 = 7
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Step 5: Collect all the output values (y-values) we found.
The output values are 4, 5, 6, and 7.
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Answer: The Range of the equation for the given x-values is {4, 5, 6, 7}.

Why It Matters

Understanding Range is crucial in fields like AI/ML, where you predict possible outcomes, or in Data Science, to see the spread of data. Engineers use it to know the limits of what a machine can produce, like the range of speeds a motor can achieve.

Common Mistakes

MISTAKE: Confusing Range with Domain. | CORRECTION: Range is the set of all possible output values (y-values), while Domain is the set of all possible input values (x-values).

MISTAKE: Forgetting to list all unique output values. | CORRECTION: Always calculate 'y' for every 'x' in the domain and ensure all distinct 'y' values are included in the Range.

MISTAKE: Assuming Range is always positive. | CORRECTION: The Range can include negative numbers, zero, or positive numbers depending on the equation and its domain.

Practice Questions

Try It Yourself

QUESTION: What is the Range of y = 2x - 1 if the x-values are {1, 2, 3}? | ANSWER: {1, 3, 5}

QUESTION: Find the Range of y = x^2 when x can be {-2, -1, 0, 1, 2}. | ANSWER: {0, 1, 4}

QUESTION: A taxi charges Rs 10 per km plus a fixed charge of Rs 20. If a customer travels 5 km, 8 km, or 10 km, what is the Range of possible charges? (Equation: Cost = 10 * distance + 20) | ANSWER: {70, 100, 120}

MCQ

Quick Quiz

If the equation is y = 3x + 5 and the input values (x) are {0, 1, 2}, what is the Range?

{0, 1, 2}

{5, 8, 11}

{3, 5, 8}

{8, 11, 14}

The Correct Answer Is:

For x=0, y = 3(0)+5 = 5. For x=1, y = 3(1)+5 = 8. For x=2, y = 3(2)+5 = 11. So the Range is {5, 8, 11}.

Real World Connection

In the Real World

In cricket analytics, if an equation predicts a batsman's score (y) based on balls faced (x), the Range would show the possible scores they could get. This helps coaches and analysts understand performance limits. Similarly, meteorologists use Range to describe the possible temperature variations in a city like Delhi over a week.

Key Vocabulary

Key Terms

DOMAIN: All possible input values for an equation | OUTPUT: The result obtained after applying the equation to an input | FUNCTION: A special type of relation where each input has exactly one output | VARIABLE: A symbol (like x or y) representing a quantity that can change

What's Next

What to Learn Next

Great job understanding Range! Next, you should explore 'Domain of an Equation' to see how it pairs with Range. Then, you can dive into 'Functions and Relations' to see how these concepts form the building blocks of advanced mathematics.