SECTION 2 3 TRANSFORMATIONS WITH REFLECTIONS I REFLECTIONS

I) REFLECTIONS Flipping an object over an axis (mirror line) No rotations/translations/change in size

II) HORIZONTAL REFLECTIONS A H. R. will occur when the X-variable is replaced with

II) VERTICAL REFLECTIONS A V. R. will occur when the Y-variable is replaced with

DIFFERENCE BETWEEN H. R AND V. R. For H. R. the negative sign will

III) INVERSE REFLECTION An inverse reflection is an inverse function: A reflection over the

REMINDERS OF INVERSE FUNCTIONS Since we switch the x & y variables for the

IV) SUMMARY Horizontal Reflection over the Y-axis Vertical Reflection over the X-axis The Y

EX: INDICATE THE TYPE OF REFLECTION FOR EACH OF THE FOLLOWING EQUATIONS Vertical Reflection!

Ex: Given that (a, b) is a point on y=f(x), find the coordinates of

Ex: Given the graph of y = f(x), draw the graph of y 8

i) Horizontal reflection ii) Vertical reflection iii) Both Horizontal & Vertical reflection iv)

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SECTION 2. 3 TRANSFORMATIONS WITH REFLECTIONS

I) REFLECTIONS Flipping an object over an axis (mirror line) No rotations/translations/change in size Vertical Reflection Reflected over the X-axis y 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 Horizontal Reflection Inverse Reflection Reflected over the Y-axis Reflected over the line y = x y 5 4 3 2 1 x -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 © Copyright All Rights Reserved Homework Depot www. BCMath. ca x y 5 4 3 2 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -2 -3 -4 -5 x

II) HORIZONTAL REFLECTIONS A H. R. will occur when the X-variable is replaced with a negative sign in front: The X-coordinates will change sign, but the Y-coordinates do NOT change at all y y 8 8 6 6 4 4 2 2 x -8 -6 -4 -2 0 -2 2 4 6 8 x -8 -6 -4 -2 0 -2 -4 -4 -6 -6 -8 -8 © Copyright All Rights Reserved Homework Depot www. BCMath. ca 2 4 6 8

II) VERTICAL REFLECTIONS A V. R. will occur when the Y-variable is replaced with a negative sign in front: Only the Y-coordinates change sign, but the X-coordinates do NOT change at all!! Y-Variable must be isolated!! y y 8 8 6 6 4 4 2 2 x -8 -6 -4 -2 0 -2 2 4 6 8 x -8 -6 -4 -2 0 -2 -4 -4 -6 -6 -8 -8 © Copyright All Rights Reserved Homework Depot www. BCMath. ca 2 4 6 8

DIFFERENCE BETWEEN H. R AND V. R. For H. R. the negative sign will be inside the function For V. R. the negative sign will be outside the function Negative sign is inside the function Negative sign is outside the function Negative sign is inside & Outside the function BOTH and Equation can be written in different forms EITHER © Copyright All Rights Reserved Homework Depot www. BCMath. ca or

III) INVERSE REFLECTION An inverse reflection is an inverse function: A reflection over the line y = x An inverse reflection occurs when the X-variable & Y-variable switches their position. Then the Y-variable is isolated Ex: Given the function f(x), find the inverse © Copyright All Rights Reserved Homework Depot www. BCMath. ca

REMINDERS OF INVERSE FUNCTIONS Since we switch the x & y variables for the inverse reflection, the domain and range will also change When graphing the inverse function, Take several points on the original function Switch the x-coordinates with the y-coordinates The new points created can be used to generate the graph of the inverse function © Copyright All Rights Reserved Homework Depot www. BCMath. ca

IV) SUMMARY Horizontal Reflection over the Y-axis Vertical Reflection over the X-axis The Y variable is always isolated, so the Negative sign is often moved to the other side Inverse Reflection over the line y=x © Copyright All Rights Reserved Homework Depot www. BCMath. ca

Ex: Given that (a, b) is a point on y=f(x), find the coordinates of a point on the function: V. R. H. R. Therefore, a new coordinate in the function will be: V. R. I. R. H. R. Therefore, a new coordinate in the function will be: © Copyright All Rights Reserved Homework Depot www. BCMath. ca

i) Horizontal reflection ii) Vertical reflection iii) Both Horizontal & Vertical reflection iv) Inverse reflection