# Unit 8Modeling with Functions

## Lesson 1

### Learning Focus

Explain function transformations across all function types.

### Lesson Summary

In this lesson, we explored the transformations of functions by comparing tables of data of parent functions and transformations of those parent functions. We found that all functions are transformed in the same ways, and we looked for explanations for why horizontal transformations—such as shifting left or right, or stretching or shrinking horizontally—behave the way they do.

## Lesson 2

### Learning Focus

Predict and examine the graphical effects of adding or multiplying functions from two different function families.

### Lesson Summary

In this lesson, we observed what happens when we combine two different function types by adding or multiplying them together. We also noticed what happens to the portion of a graph of a function that lies below the -axis when we take the absolute value of the function.

## Lesson 3

### Learning Focus

Write equations that would produce given graphs created by adding or multiplying two functions together.

### Lesson Summary

In this lesson, we wrote equations to fit given graphs and tables of data that involved combining function types or reflecting functions to model the context.

## Lesson 4

### Learning Focus

Examine function composition in the context of a real-world scenario.

### Lesson Summary

In this lesson, we learned a new operation for combining functions called function composition. We use function composition when the input for one function is the output of another function.

## Lesson 5

### Learning Focus

Write and evaluate composite functions.

### Lesson Summary

In this lesson, we decomposed complex function rules into sequences of smaller functions that could be evaluated to give the same results as more complicated functions.

## Lesson 6

### Learning Focus

Combine functions defined by graphs or tables.

### Lesson Summary

In this lesson, we learned how to graph the sum or product of two functions which are only defined by their graphs. We also learned how to complete a table of values for the sum, product, inverse or composition of functions defined only by a table. We also modeled a context by selecting whether we should use a composition function or a combination function.