**GRADE 12 UNIVERSITY FUNCTIONS**

Functions and Rate of Change

Functions and Rate of Change

## Learning Goal:

**The goal of this unit is to:**

1) compare characteristics of functions and solve problems by modeling and reasoning with functions

2) demonstrate an understanding of average and instantaneous rate of change and determine value over a given interval (average rate of change) or for a given point (instantaneous rate of change)

1) compare characteristics of functions and solve problems by modeling and reasoning with functions

2) demonstrate an understanding of average and instantaneous rate of change and determine value over a given interval (average rate of change) or for a given point (instantaneous rate of change)

## Success Criteria:

**By the end of this unit, I will be able to:**

**- Graph and apply transformations to 5 basic functions including y=x^2, y=x^3, y=x^4, y=|x|, y = sqrt(x)**

- Understand properties of inverse functions both algebraically and graphically

- Understand properties of inverse functions both algebraically and graphically

**- Analyze the properties and domain and range of piecewise functions**

- Determine the average rate of change over a given interval of a function

- Determine the instantaneous rate of change at a given point of a function

- Determine the average rate of change over a given interval of a function

- Determine the instantaneous rate of change at a given point of a function

**- Use your knowledge of rate of change to confirm maximum or minimum values of a function**

- Use rate of change to determine the increasing and decreasing nature of a function

- Use rate of change to determine the increasing and decreasing nature of a function