Reflections

ReflectionAnimationAll

In general, multiplying a function by a negative sign creates a reflection:

y = f(x) or y = f(x)

 

PUSHING THE Y-REFLECTION BUTTON
FLIPS FUNCTIONS ABOUT THE X-AXIS

y = f(x)

Do you see how the negative sign is on the outside of the function… affecting the y-value of the function?

Example: y = |x| will flip the function about the x-axis

ReflectionY

If the negative sign belongs to the y-value

the graph will reflect about the x-axis.

 

PUSHING THE X-REFLECTION BUTTON
FLIPS FUNCTIONS ABOUT THE Y-AXIS

y = f(x)

Do you see how the negative sign is on the inside of the function… affecting the x-value of the function?

Example: y = |x| will flip the function about the y-axis

ReflectionX

If the negative sign belongs to the x-value

the graph will reflect about the y-axis.


Remember Reflections: They are opposites

If the negative sign belongs to the y, then the graph will flip about the x-axis.
If the negative sign belongs to the x, then the graph will flip about the y-axis.

Now let’s Put it All Together