Sketch graphs of functions given qualitative descriptions of the relationship.
Two graphs representing a student’s movements are shown below. For each graph,
Two stories are shown below. For each one, draw a graph to represent the functional relationship between the two quantities.
Story 1: Distance from home vs. Time
You leave home and walk to the corner store. At the store, you spend a few minutes shopping, but then realize that you forgot your wallet at home. You run home, find your wallet immediately, and then run back to the store where you pay for your items. You leave the store and slowly walk away in the opposite direction of your home, toward the basketball court. Once you get to the court, you look for your friend for a few minutes, but when you realize that he’s not there, you walk quickly back home.
Story 2: Temperature vs. Time
At 8 AM on a summer day, the temperature in Hartford, Connecticut, was 60°F. By 10 AM, the temperature had risen 10°F, where it stayed until 12 PM. From noon to 3 PM, the temperature rose to 85°F, after which it dropped at a steady rate until it hit 65°F at 9 PM.
Nina rides her bike from her home to school, passing by the library on the way and traveling at a constant speed for the entire trip. (See map below.)
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
A child at a park sees a slide. She runs across the playground to the slide and slowly climbs up the stairs. At the top of the stairs, she pauses for a moment and then slides down to the bottom.
Sketch two graphs for the situation: one that shows the child’s distance from the stairs of the slide as a function of time, and the other that shows the child’s speed as a function of time.