2 5 Graphical Transformations transformation a change to

2. 5 Graphical Transformations transformation: a change to a graph in a predictable way translation: a shift or a slide in the graph reflection: a flip of the graph

Translations If y=f(x) then: y=f(x-c) is a horizontal shift right c units. y=f(x+c) is a horizontal shift left c units. y=f(x)+c is a vertical shift up c units. y=f(x)-c is a vertical shift down c units.

Ex 1: Describe the transformation to occurs in the equation. that It is a vertical translation up three units.

Ex 2: Describe the transformation to occurs in the equation. that It is a horizontal translation right two units.

Ex 3: Describe the transformation to occurs in the equation. that It is a vertical translation down 4 units and a horizontal translation left 6 units.

Ex 4: This is a vertical translation down 3 units and a horizontal translation left one unit.

Reflections If y=f(x) then: y=-f(x) is a reflection across the x-axis y=f(-x) is a reflection across the y-axis

Ex 5: Find an equation for the reflection of across each axis. Across the x-axis: Across the y-axis:

Compressions / Stretches If y=f(x) then: y=f(x/a) is a horizontal stretch by a factor of a if a>1. y=f(x/a) is a horizontal compression by a factor of a if 0<a<1. y=a∙f(x) is a vertical stretch by a factor of a if a>1. y=a∙f(x) is a vertical compression by a factor of a if 0<a<1.

Ex 6: Show the equation for a vertical compression of y=x 2 by a factor of 1/2, and a horizontal compression by a factor of 2. Vertical Compression Horizontal Stretch

2. 5 HW Assignment Pg. 112: #s 7 -30 all