Analyzing Real-World Function Graphs

Each graph shows the distance as a function of time. One graph shows the function when Mr. Dilla is driving in has neighborhood. The other graphs represent Mr. Dilla driving on major city streets and highways. Which description matches each graph below?

*Hint: Find the rate of change for each graph!

To represent some real-world situations, you may need to break a graph into pieces to show a sequence of events.

Be careful when you interpret the meaning of the word “constant”:

If you see a line that slants up, it means that the function is increasing at a constant rate. (As time increases, the distance increases)

If the line slants down, it means that the function is decreasing at a constant rate. (As time increases, the distance decreases)

If the line is horizontal, the graph is neither increasing nor decreasing. (As time increases, the distance doesn’t change.)

Example: On Thursday, Maksim went for a long nature walk, stopping for lunch at one point. The graph represents his walk.

Describe what Maksim did during eachinterval shown.

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Example: The graph shows the number of calories Janis burnedduring an 18-minute workout. During which interval did she burnthe most? The least?

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Example: The graph shows the distance that Kathy travelled from home and back to attend a conference. Describe what is possibly going on during each interval of the graph.

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Example: Cara went roller skating in her neighborhood. The graph shows the distance she traveled to and from her home. Describe, in detail, what is shown by the graph.

Example: Mike traveled to his grandfather’s. He traveled at a constant rate for the first 20 minutes, for a distance of 1 mile. Then he stopped for 20 minutes to have a snack. Finally he traveled at a constant rate over the next 40 minutes for a distance of 8 miles and stopped when he got to his grandfather’s house. Create a function graph of Mike’s trip.

Example: Mike traveled to his grandfather’s. He traveled at a constant rate for the first 20 minutes, for a distance of 1 mile. Then he stopped for 20 minutes to have a snack. Finally he traveled at a constant rate over the next 40 minutes for a distance of 8 miles and stopped when he got to his grandfather’s house. Create a function graph of Mike’s trip.