Even More Graphs of Functions
Let’s draw a graph from a story.
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.
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.
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 \(\frac12\) \(A\) \(16\pi\) \(100\pi\)
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?