# Lesson 4 Water Wonderland Solidify Understanding

## Learning Focus

Interpret the graphs and equations of functions.

Write equations for the graph of functions.

Combine two linear functions.

How does function notation connect to a graph?

What connections can be made with function notation and a story context?

How do I combine functions graphically and algebraically?

## Open Up the Math: Launch, Explore, Discuss

Aly and Dayne work at a water park and are required to drain the water at the end of each month for the ride they supervise. Each uses a pump to remove the water from the small pool at the bottom of their ride. The graph given represents the amount of water in Aly’s pool,

### 1.

Make as many observations as possible with the information given in the graph.

Dayne figured out that the pump he uses drains water at a rate of

### 2.

Write the equation to represent the draining of Dayne’s pool,

### 3.

Based on this new information, correctly label the graph shown.

### 4.

What values of

### 5.

What output values make sense in this situation? Write the range of the function that represents the amount of water in Dayne’s pool.

### 6.

Write the equation that represents the draining of Aly’s pool,

Equation:

Domain:

Range:

Based on the graph and corresponding equations for each pool, answer the following questions.

### 7.

When is

### 8.

Find

### 9.

If

### 10.

When is

This month, Aly and Dayne decided to work together by putting both pumps in the pool at the same time to drain their pools and created the equation:

### 11.

What does

### 12.

Graph

### 13.

Write the equation for the function

### 14.

Should the algebraic equation of

### 15.

Use both the graphical and the algebraic representation to describe key features of and explain what each feature means (each intercept, domain and range for this situation and for the equation, maxima and minima, whether or not is a function, etc.)

Domain:

What it means in this context:

Range:

What it means in this context:

Interval(s) of increase:

What it means in this context:

Interval(s) of decrease:

What it means in this context:

What it means in this context:

What it means in this context:

Rate of change:

What it means in this context:

Continuous? Why?

Function? Why?

### 16.

Explain why adding the two values of the

### 17.

Can a similar method be used to find the

## Ready for More?

Fletcher, another employee, decided to start draining the pools before Aly and Dayne showed up for work. When Aly and Dayne arrived, there were already

## Takeaways

Function vocabulary and notation:

## Lesson Summary

In this lesson we wrote the equation of two functions given graphically and with a story context. We connected the domain and range to the context and the graph. We deepened our understanding of function notation, learning to interpret the notation for graphs, tables, and equations. We learned that functions can be added together both graphically and algebraically.

Solve the equations for

### 1.

### 2.

### 3.

List the key features of the function provided in the graph.