# Lesson 6

Even More Graphs of Functions

### Problem 1

Match the graph to the following situations (you can use a graph multiple times). For each match, name possible independent and dependent variables and how you would label the axes.

- Tyler pours the same amount of milk from a bottle every morning.
- A plant grows the same amount every week.
- The day started very warm but then it got colder.
- A carnival has an entry fee of $5 and tickets for rides cost $1 each.

### Solution

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### Problem 2

Jada fills her aquarium with water.

The graph shows the height of the water, in cm, in the aquarium as a function of time in minutes. Invent a story of how Jada fills the aquarium that fits the graph.

### Solution

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### Problem 3

Recall the formula for area of a circle.

- Write an equation relating a circle’s radius, \(r\), and area, \(A\).
- Is area a function of the radius? Is radius a function of the area?
- Fill in the missing parts of the table.
\(r\) 3 \(\frac12\) **\(A\)**\(16\pi\) \(100\pi\)

### Solution

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(From Unit 6, Lesson 4.)### Problem 4

The points with coordinates \((4,8)\), \((2,10)\), and \((5,7)\) all lie on the line \(2x+2y=24\).

- Create a graph, plot the points, and sketch the line.
- What is the slope of the line you graphed?
- What does this slope tell you about the relationship between lengths and widths of rectangles with perimeter 24?