scaling

Examples of scaling in the following topics:

• Solving Problems with Logarithmic Graphs

  • Here are some examples of functions graphed on a linear scale, semi-log and logarithmic scales.
  • The top left is a linear scale.
  • The bottom right is a logarithmic scale.
  • The top right and bottom left are called semi-log scales because one axis is scaled linearly while the other is scaled using logarithms.
  • Top Left is a linear scale, top right and bottom left are semi-log scales and bottom right is a logarithmic scale.

• Stretching and Shrinking

  • In algebra, equations can undergo scaling, meaning they can be stretched horizontally or vertically along an axis.  
  • First, let's talk about vertical scaling.  
  • In general, the equation for vertical scaling is:
  • Now lets analyze horizontal scaling. 
  • In general, the equation for horizontal scaling is:

• Transformations of Functions

  • The four main types of transformations are translations, reflections, rotations, and scaling.
  • Scaling is a transformation that changes the size and/or the shape of the graph of the function.  
  • Differentiate between three common types of transformations: reflections, rotations, and scaling

• Introduction to Ellipses

  • To do this, we introduce a scaling factor into one or both of the $x$-$y$ coordinates.
  • Let's start by dividing all $x$ coordinates by a factor $a$, and therefore scaling the $x$ values.
  • Similarly, we can scale all the values of $y$ by a factor $b$ (we also assume $b > 1$).
  • If we had used scaling factors that were less than one, it would have compressed the shape instead of stretching it further out.

• Inconsistent and Dependent Systems

  • are dependent — they are the same equation when scaled by a factor of two, and they would produce identical graphs.

• Cofactors, Minors, and Further Determinants

  • The determinant is the sum of the signed minors of any row or column of the matrix scaled by the elements in that row or column.

• Common Bases of Logarithms

  • Logarithmic scales reduce wide-ranging quantities to tiny scopes.
  • The pH scale measures how acidic or basic a substance is.

• What Are Polynomials?

  • They have the form of a sum of scaled powers of a variable.

• Inconsistent and Dependent Systems in Two Variables

  • Also note that they are the same equation scaled by a factor of two; in other words, the second equation can be derived from the first.

• Matrices and Row Operations

  • Row multiplication (scale): Multiply a row of a matrix by a nonzero constant.