Essential Question:  What is the relationship between transformations and their equations and graphs?

Unit Rationale:  Interpretation of graphs of functions and relations, including using function notation and function families, is a prerequisite to applying transformation to those graphs.

As a result of this unit, students will be able to:

Ø  Write the equation from graphs using transformation

Ø  Graph the transforms equation

Ø  Identify domain and range for a function

Ø  Use and understand function notation

Ø  Apply transformation concepts to model situations

Vocabulary:

·         Relation, function

·         Transformations, image

·         Discrete, continuous

·         Function notation

·         Translation, reflection, dilation

·         Parabola

·         Line of symmetry

·         Vertex

·         Parent function

·         Quadratic function

·         Square root function

·         Absolute value function

Focus Standards:

A2.1.C  Solve problems that can be represented by quadratic functions and equations.

A2.5.A  Construct new functions using transformation f(x-h), f(x) +k, CF(x) and by adding and subtracting functions and describe the effect on the original graph

A2.5.B  Plot points, sketch, and describe the graphs of functions of the form f(x)=a (x-c)^1/2 +d, and solve related equations.

Support Standards:

A2.1.A  Select and justify functions and equations to model and solve problems.

Reasoning, Problem Solving, and Communication Standards:

A2.8.D  Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems.

A2.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.