What is the Range of Algebraic Expressions?

S3-SA1-0787

Grade Level:

Class 6

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

Definition

What is it?

The 'range' of an algebraic expression tells us all the possible values that the expression can take. It's like finding all the possible scores a cricketer can make in a series of matches, from the lowest to the highest.

Simple Example

Quick Example

Imagine you sell chai, and the price of one cup is 'x' rupees. If 'x' can be any whole number from 10 to 20 rupees (depending on the flavour), then the range of the expression 'x' is all numbers between 10 and 20, including 10 and 20.

Worked Example

Step-by-Step

Let's find the range for the expression '2x + 1' if 'x' can be 1, 2, or 3.

Step 1: Substitute the first value of x (which is 1) into the expression.
2(1) + 1 = 2 + 1 = 3
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Step 2: Substitute the second value of x (which is 2) into the expression.
2(2) + 1 = 4 + 1 = 5
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Step 3: Substitute the third value of x (which is 3) into the expression.
2(3) + 1 = 6 + 1 = 7
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Step 4: List all the results you got.
The values are 3, 5, and 7.
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Answer: The range of the expression '2x + 1' for x = 1, 2, 3 is {3, 5, 7}.

Why It Matters

Understanding range helps in fields like Data Science to know the spread of data, or in Engineering to understand the limits of a machine's performance. It's crucial for careers in AI/ML where you predict possible outcomes or in Economics to analyze price variations.

Common Mistakes

MISTAKE: Not substituting all possible values for the variable. | CORRECTION: Always substitute every given value for the variable into the expression to find all possible outputs.

MISTAKE: Making calculation errors when substituting values. | CORRECTION: Double-check your basic arithmetic (addition, subtraction, multiplication) after substituting each value.

MISTAKE: Confusing 'range' with 'domain'. | CORRECTION: 'Domain' refers to the possible input values for the variable, while 'range' refers to the possible output values of the entire expression.

Practice Questions

Try It Yourself

QUESTION: What is the range of the expression 'y - 5' if y can be 10, 12, or 15? | ANSWER: {5, 7, 10}

QUESTION: Find the range of '3z' if z can be 0, 1, 2, 3. | ANSWER: {0, 3, 6, 9}

QUESTION: If the expression is 'x^2 + 2' and x can be -1, 0, or 1, what is the range? (Hint: (-1)^2 is 1) | ANSWER: {2, 3}

MCQ

Quick Quiz

What is the range of the expression 'x + 7' if x can be 2, 4, 6?

{2, 4, 6}

{7, 9, 11}

{9, 11, 13}

{14, 28, 42}

The Correct Answer Is:

When x=2, x+7=9. When x=4, x+7=11. When x=6, x+7=13. So, the range is {9, 11, 13}.

Real World Connection

In the Real World

Imagine a delivery app like Swiggy or Zomato. The delivery time for an order can vary. If the delivery time expression is '15 + 2k' (where k is traffic factor), knowing the range of k helps the app predict the fastest and slowest possible delivery times for customers. This is crucial for managing expectations and improving service.

Key Vocabulary

Key Terms

ALGEBRAIC EXPRESSION: A mathematical phrase that contains variables, numbers, and operations. | VARIABLE: A symbol (like x, y, z) that represents a value that can change. | SUBSTITUTE: To replace a variable with a specific number. | DOMAIN: The set of all possible input values for the variable in an expression.

What's Next

What to Learn Next

Now that you understand range, you can explore 'Domain of Algebraic Expressions' to learn about the possible input values. This will help you fully understand how expressions behave and what values they can produce.