We can use algebraic operations to rewrite expressions, including polynomial expressions. When we rewrite polynomial expressions, the representations look different but still represent the same expression.

Where else have you seen this type of transformation—when something appears different, but its meaning remains the same?

This type of transformation can also be found in the associations of sets, in the calculation of square roots and in the calculation with different units of measurement and the Geometric Transformation.

Step-by-step explanation:

A Geometric Transformation, also known as Transformation in the Plane or Movement in the Plane, is a function that corresponds to each point on the plane, another point on the same plane called Image. In general, a Transformation is a geometric operation that allows finding or building a new figure from one that was initially given. The new figure is called homologous or transformed from the original.

When we work on Geometric Transformations, it is important to take into account the notation to use; then if A is a point on the α plane, to which a transformation T is applied, then A´, which also belongs to the α plane, is its counterpart or transformed if there is such an application that converts A to A´. We will notice this as well

  T (A) = A´

and it reads “the homologue of A by application of the transformation T is A´.”

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is