A glide reflection is a composition of a line reflection and a translation that is parallel to the line of reflection. Unlike some composition of transformations, a glide reflection IS . Therefore, the line reflection and translation can be done in any .

" a glide reflection IS commutative. Therefore, the line reflection and translation can be done in any order."

Step-by-step explanation:

Transformations can be written as operators that act on functions or shapes.

For example, we can define the horizontal translation operator as:

T(k)

And if we apply this to a function, we get:

T(k)[ f(x) ] = f(x - k)

Now, the operators are not necessarily commutative.

This means that if we have two operators:

K and L

is not the same:

K[ L[ f(x) ]]

than:

L[ K[ f(x) ]]

An example of this can be a reflection across the y-axis and a horizontal translation, that composition is non-commutative.

Now, let's go to our case.

A glide reflection is commutative, so we can perform the transformations in any order, then the statement is:

" a glide reflection IS commutative. Therefore, the line reflection and translation can be done in any order."

21

jk it's 20

step-by-step explanation:

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: