Answer:
These transformations do not change the size of the image.
Step-by-step explanation:
By going over the different properties of translations, reflections and rotations, we can determine what exactly is common about each of these.
- Translations: the shifting of a function on the coordinate plane without any change in congruence, shape or size.
- In algebra, translations are seen most often in quadratic and linear functions, and always by adding or subtracting a number the function's [tex]x[/tex] and/or [tex]y[/tex] values.
- ex.) In the parent function of standard-form quadratic equations, [tex]f(x)=ax^2+bx+c[/tex], the value [tex]c[/tex] would be considered a value that determines the function's vertical translation. It is a value that would move the equation up or down if changed.
- Reflection: the flipping of a function without any change of its overall shape or size.
- In algebra, a reflection is usually seen in vertical reflections across the [tex]x[/tex]-axis.
- ex.) The [tex]a[/tex] in standard-form quadratic equations is an example of a reflection across the [tex]x[/tex]-axis. If it's sign is changed (if it is changed from negative to positive and vise-versa), then the equation would be flipped across the [tex]x[/tex]-axis.
- Rotation: the change of a function's rotation without any change in its size, shape or location.
- Rotations, are most often seen in linear equations with a line's slope.
- ex.) In the standard form linear function, [tex]f(x)=mx+b[/tex], [tex]m[/tex] or the line's slope changes the rotation of the function.
Translation, reflection and rotation all do not change the size of the function/shape they are acting on. Thus, Answer D is correct.
