Lesson 6
Even More Graphs of Functions
Let’s draw a graph from a story.
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.
![Three graphs, linear, piecewise, curve.](https://cms-im.s3.amazonaws.com/iiFtCA5ESC8mnQL1dMrMXrd3?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.B.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.B.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c7256396cc1c57b1cba3a3578b9b303f69c012eeef7bb57a1212bd603cb830af)
- 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.
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.
![Coordinate plane, time, minutes, 0 to 10, height, centimeters, 0 to 35 by fives. Segments connect points 0 comma 0, to 2 comma 10, to 3 comma 10, to 5 comma 30, to 7 comma 25, to 10 comma 25.](https://cms-im.s3.amazonaws.com/oCtmQWQmVVY9XokMiwo6gJPx?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.B.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.B.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=bb40824dce4d728873eb483f71fbaf27ab25b0732b3ada103a2e212e6c78a615)
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 \(\frac12\) \(A\) \(16\pi\) \(100\pi\)
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?
![A blank grid.](https://cms-im.s3.amazonaws.com/KvJuApZNR8A8xQLScWdsiRrU?response-content-disposition=inline%3B%20filename%3D%228-8.3.blank.grid.asdf.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.blank.grid.asdf.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182415Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9595f667a98d39e2634c97f4165314b3db8135d7337eb3f0d648ea49eed4af5d)