Warm Up Every weekday morning, cousins Ainsley, Jack, and Caleb are given a different amount of money for lunch by their parents. Ainsley gets $3, Jack receives $4, and Caleb gets $5. On the way to school, they stop by their Grandpa Ray’s house to say hello. He always gives them each $2 more for lunch. By the time the cousins reach the bus stop, they each have more money than when they left the house. Mathematically, one way to describe this story would be to assign each of the cousins a value, and define Grandpa Ray as a function. Example: Let Ainsley = $3, Jack = $4, and Caleb = $5. We can then define Grandpa Ray as a function, R, where R “of” x dollars, written R(x), is x + $2. Then we can say R(Ainsley) = R($3) = $5, R(Jack) = R($4) = $6, and R(Caleb) = R($5) = $7. The actual cost of lunch for each cousin is $2. Using the values assigned to the cousins in the example and defining lunch as the function, L, use function notation to symbolize paying for lunch.

Transformations as Functions

Definitions Transformation: a change in a geometric figure’s position, shape, or size Translation: slide Reflection: flip Rotation: turn Congruent: figures are congruent if they have the same shape, size, lines, and angles

Preimage: the original figure before undergoing a transformation Image: the new, resulting figure after a transformation Isometry: a transformation in which the preimage and image are congruent

Transformations as Functions Each coordinate on the coordinate plane is a real number pair, (x,y). When a transformation is applied to a set of points, then all points in the set are moved. For example if T(x,y) = (x+h, y+k), then T(ΔABC) would be:

Identity Function

One-to-one: each point in the set of points will be mapped to exactly one other point

Horizontal stretches and dilations are not isometric.

1. Given the point P (5, 3) and T(x, y) = (x + 2, y + 2), what are the coordinates of T(P)?

2. Given ABC : A(5,2), B(3,5), and C (2,2), and the transformation T(x, y) = (x, –y), what are the coordinates of the vertices of T (ABC)? What kind of transformation is T?