Step Graphs Worksheet
Explore step graphs, their properties, and real-world applications with this Grade 11 math worksheet. Practice interpreting and creating step graphs.
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Step Graphs Worksheet
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. Define what a step graph is and provide an example of a real-world scenario where a step graph would be an appropriate representation of data.
2. The graph below shows the cost of shipping a package based on its weight. Use the graph to answer the following questions.
a) What is the cost to ship a package that weighs exactly 2 kg?
b) What is the cost to ship a package that weighs 3.5 kg?
c) If a customer paid $10 for shipping, what is the possible range of weights for their package?
3. Complete the following statements about step graphs:
a) A step graph is characterized by its segments, which represent a constant value over an interval.
b) The points at which the graph 'jumps' from one constant value to another are called .
c) An open circle on a step graph indicates that the endpoint is in the interval, while a closed circle indicates it is .
4. Which of the following functions would most likely be represented by a step graph?
The height of a growing plant over time.
The temperature of water as it boils.
The cost of a taxi ride based on the distance traveled, where the fare increases at fixed distance intervals.
The speed of a car accelerating uniformly.
5. A local parking garage charges the following rates:
- Up to 1 hour: $3.00 - Over 1 hour up to 2 hours: $5.00 - Over 2 hours up to 4 hours: $8.00 - Over 4 hours up to 6 hours: $12.00
Create a step graph to represent the parking cost as a function of time parked (in hours). Label your axes clearly.
6. Explain the concept of discontinuity in the context of a step graph. What do the open and closed circles signify at these points of discontinuity?