#### MAT-HS.F-BF.01

 MAT-HS Targeted Standards(F) Concept: Function(BF) Domain: Building FunctionsCluster: Build a function that models a relationship between two quantities MAT-HS.F-BF.01 Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations.For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.

## Student Learning Targets:

### Knowledge Targets

• I can recognize the notation for the composition of functions.
• I can recognize the proper notation for inverse functions.

### Reasoning Targets

• I can determine the inverse of a function.
• I can interpret the results of the horizontal line test.
• I can verify whether two functions are inverses of each other using compositions.

### Skills (Performance) Targets

• I can graph a linear equation.
• I can manipulate the form of a linear equation.
• I can identify a linear equation.
• I can use algebraic expressions, equations or inequalities involving one or two variables to represent geometric relationships.
• I can perform composition of algebraic functions.
• I can demonstrate the inverse of an algebraic function graphically.
• I can perform the horizontal line test to determine if the inverse of a function exists.
• I can combine function types, such as linear and exponential, using arithmetic operations.

### Product Targets

• I can write a functions that describes a relationship between two quantities.
• I can write an explicit or recursive expression or describe the calculations needed to model a function given a situation.

## Proficiency Scale

 Score Description Sample Activity 4.0 In addition to Score 3.0, the student demonstrates in-depth inferences and applications regarding more complex material that go beyond end of instruction expectations. - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” The student demonstrates no major errors or omissions regarding any of the information and processes that were end of instruction expectations. - 2.5 The student demonstrates no major errors or omissions regarding the simpler details and processes (Score 2.0 content) and partial knowledge of the more complex ideas and processes (Score 3.0 content). 2.0 The student demonstrates no major errors or omissions regarding the simpler details and processes but exhibits major errors or omissions regarding the more complex ideas and processes (Score 3.0 content). - 1.5 The student demonstrates partial knowledge of the simpler details and processes (Score 2.0 content) but exhibits major errors or omissions regarding the more complex ideas and procedures (Score 3.0 content). 1.0 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) and some of the more complex ideas and processes (Score 3.0 content). - 0.5 With help, the student demonstrates a partial understanding of some of the simpler details and processes (Score 2.0 content) but not the more complex ideas and processes (Score 3.0 content). 0.0 Even with help, the student demonstrates no understanding or skill. -

## Resources

 Web Vocab explicit recursive linear exponential function