Modulus Function - Graph | Don't Memorise

TL;DR

Modulus function gives the absolute value of a number, always non-negative, represented graphically with symmetry.

Transcript

what is the modulus of a number the modulus of a number is nothing but its absolute value we have learnt that the absolute value gives us the distance of a number from zero without considering the direction in which the number lies so in other words the absolute value or the modulus of a number gives us the magnitude of a number what sign can the m... Read More

Key Insights

• #️⃣ Modulus function gives the absolute value of a number.
• 🚱 It is non-negative as it represents distance from zero.
• 😍 Graphically, modulus function forms a v-shaped curve symmetric about the y-axis.
• #️⃣ Domain of the modulus function is all real numbers.
• 😫 Range of the modulus function includes the upper half of the real number set including zero.
• ☺️ The modulus function is defined as f(X) = X for X greater than or equal to zero and f(X) = -X for X less than zero.
• 😀 The modulus function graphically shows symmetry about the y-axis and has positive y-values.

Questions & Answers

Q: What is the modulus of a number?

The modulus of a number is its absolute value, representing its distance from zero without considering the direction it lies in.

Q: How is the modulus function defined?

The modulus function is defined as f(X) = X for X greater than or equal to zero and f(X) = -X for X less than zero.

Q: What does the graph of the modulus function look like?

The graph of the modulus function is a v-shaped curve opening upwards, with the vertex at the origin, and is symmetric about the y-axis.

Q: What is the domain and range of the modulus function?

The domain of the modulus function is all real numbers, while the range is the upper half of the real number set including zero.

Summary & Key Takeaways

• Modulus of a number is its absolute value, giving distance from zero.

• Modulus can be positive or zero, never negative.

• The modulus function is defined as f(X) = X for X >= 0 and f(X) = -X for X < 0.