key term - Magnitude

Definition

Magnitude refers to the size or quantity of a mathematical object, often represented as the absolute value of a number. It gives the distance of a number from zero on the number line.

5 Must Know Facts For Your Next Test

1. The magnitude of a real number is its absolute value, denoted as $|x|$ for a number $x$.
2. Magnitude is always non-negative because it represents distance.
3. In transformations, scaling by magnitude affects the steepness or width of graphs.
4. When dealing with complex numbers, magnitude is calculated using $\sqrt{a^2 + b^2}$ where $a$ and $b$ are real and imaginary parts respectively.
5. For vectors, magnitude determines their length and can be found using the Euclidean norm.

Review Questions

Related terms

Absolute Value:

The non-negative value of a real number without regard to its sign.

Transformation: A change made to the position or size of a function's graph including translations, reflections, stretches, and compressions.

Euclidean Norm: The length (or 'magnitude') of a vector in Euclidean space, often calculated using $\sqrt{x_1^2 + x_2^2 + ... + x_n^2}$ for an n-dimensional vector.