# Alg1.4 Functions

### Lesson 1

- I can explain when a relationship between two quantities is a function.
- I can identify independent and dependent variables in a function, and use words and graphs to represent the function.
- I can make sense of descriptions and graphs of functions and explain what they tell us about situations.

### Lesson 2

- I can use function notation to express functions that have specific inputs and outputs.
- I understand what function notation is and why it exists.
- When given a statement written in function notation, I can explain what it means in terms of a situation.

### Lesson 3

- I can describe the connections between a statement in function notation and the graph of the function.
- I can use function notation to efficiently represent a relationship between two quantities in a situation.
- I can use statements in function notation to sketch a graph of a function.

### Lesson 4

- I can make sense of rules of functions when they are written in function notation, and create tables and graphs to represent the functions.
- I can write equations that represent the rules of functions.

### Lesson 5

- I can use technology to graph a function given in function notation, and use the graph to find the values of the function.
- I know different ways to find the value of a function and to solve equations written in function notation.
- I know what makes a function a linear function.

### Lesson 6

- I can identify important features of graphs of functions and explain what they mean in the situations represented.
- I understand and can use the terms “horizontal intercept,” “vertical intercept,” “maximum,” and “minimum” when talking about functions and their graphs.

### Lesson 7

- I understand the meaning of the term “average rate of change.”
- When given a graph of a function, I can estimate or calculate the average rate of change between two points.

### Lesson 8

- I can explain the average rate of change of a function in terms of a situation.
- I can make sense of important features of a graph and explain what they mean in a situation.
- When given a description or a visual representation of a situation, I can sketch a graph that shows important features of the situation.

### Lesson 9

- I can compare the features of graphs of functions and explain what they mean in the situations represented.
- I can make sense of an equation of the form $f(x)=g(x)$ in terms of a situation and a graph, and know how to find the solutions.
- I can make sense of statements about two or more functions when they are written in function notation.

### Lesson 10

- I know what is meant by the “domain” and “range” of a function.
- When given a description of a function in a situation, I can determine reasonable domain and range for the function.

### Lesson 11

- When given a description of a function in a situation, I can determine reasonable domain and range for the function.

### Lesson 12

- I can make sense of a graph of a piecewise function in terms of a situation, and sketch a graph of the function when the rules are given.
- I can make sense of the rules of a piecewise function when they are written in function notation and explain what they mean in the situation represented.
- I understand what makes a function a piecewise function.

### Lesson 13

- Given a set of numerical guesses and a target number, I can calculate absolute errors and create a scatter plot of the data.
- I can analyze and describe features of a scatter plot that shows absolute error data.
- I can describe the general relationship between guesses and absolute errors using words or equations.

### Lesson 14

- I can describe the effects of adding a number to the expression that defines an absolute value function.
- I can explain the meaning of absolute value function in terms of distance.
- When given an absolute value function in words or in function notation, I can make sense of it, and can create a table of values and a graph to represent it.

### Lesson 15

- I understand the meaning of “inverse function” and how it could be found.
- When given a linear function that represents a situation, I can use words and equations to describe the inverse function.

### Lesson 16

- I can explain the meaning of an inverse function in terms of a situation.
- When I have an equation that defines a linear function, I know how to find its inverse.

### Lesson 17

- I can write a linear function to model given data and find the inverse of the function.
- When given a linear function defined using function notation, I know how to find its inverse.