Even More Graphs of Functions

Warmup

Activity #1

Choose a Graph that Matches the Situation.

Jada is training for a swimming race. The more she practices, the less time it takes for her to swim one lap.

(1.) Name the independent and dependent variables.

• Pick the graph that best fits the situation, or sketch the graph if one isn’t provided.
• Label the axes.

(2.) Which quantity is a function of which? Be prepared to explain your reasoning.

Andre adds some money to a jar in his room each week for 3 weeks and then takes some out in week 4.

(1). Name the independent and dependent variables.

• Pick the graph that best fits the situation, or sketch the graph if one isn’t provided.
• Label the axes.

(2.) Which quantity is a function of which? Explain your reasoning.

Activity #2

Create a Visual Display.

You will use the tools in the applet below to create a visual display that shows your response to the question.

Here is a story: “Noah was at home. He got on his bike and rode to his friend’s house and stayed there for awhile. Then he rode home again. Then he rode to the park. Then he rode home again.”

• Sketch a graph of this story.

What are the two quantities?

• Label the axes with their names and units of measure. (For example, if this were a story about pouring water into a pitcher, one of your labels might say “volume (liters)”).
• Note: To change the values on the axes, select the Move Graphics tool .
• Click near the end of the axis you want to change, and drag it to grow or shrink it.

(1.) Which quantity is a function of which? Explain your reasoning.

(2.) Based on your graph, is his friend’s house or the park closer to Noah’s home? Explain how you know.

(3.) Read the story and all your responses again. Does everything make sense? If not, make changes to your work.

Activity #3

Find the Line when Slope is Given.

• Use the red points on the line in the applet below to draw the graph.
• When you are satisfied about the line, click .
• Continue to practice as much as you can.

Challenge #1

Jada fills her aquarium with water. The graph below shows the height of the water, in cm, in the aquarium as a function of time in minutes.

Challenge #2

(1.) Write an equation relating a circle’s radius, r, and area,  A.

(2.) Is area a function of the radius?

(3.) Is radius a function of the area?

(4.) Fill in the missing parts of the table below.

Challenge #3

The points with coordinates (4,8), (2,10), and (5,7) all lie on the line 2x + 2y = 24. Plot the points, and create the graph. Label your axes.

(1.) What is the slope of the line you graphed?

(2.) What does this slope tell you about the relationship between lengths and widths of rectangles with perimeter 24?