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Analyzing Maria's Bike Journey: Distance Graph and Function Characteristics

The provided graph illustrates Maria's journey as she cycled to meet friends and run errands for her mom before returning home. This activity prompts questions about the horizontal lines representing stationary periods, the sections of the graph depicting her errands, and her changing travel pace. Students will explore concepts of intercepts, domains, ranges, and function characteristics such as increasing, decreasing, and continuity. By creating a narrative to match the graph and analyzing its features, learners will enhance their understanding of graphs in real-life contexts.

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Analyzing Maria's Bike Journey: Distance Graph and Function Characteristics

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  1. The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home. • What do the horizontal lines on the graph represent? • Where in the graph shows her taking care of the 2 errands? • Compare how she traveled at the beginning to how she traveled at the very end. • Create Maria’s story so that it matches the graph.

  2. Review HW

  3. Characteristics of Functions

  4. Intercepts • x-intercept – the point at which the line intersects the x-axis at (x, 0) • y-intercept – the point at which the line intersects the y-axis at (0, y)

  5. Find the x and y intercepts, then graph. -3x + 2y = 12

  6. Increasing, Decreasing, or Constant • Sweep from left to right and notice what happens to the y-values • Increasing goes up (L to R) • Decreasing falls down (L to R) • Constant is a horizontal graph

  7. Continuous vs Discrete • Continuous has NO breaks • Discrete has gaps or breaks

  8. Extrema • Minimum Point – leastvalue of the function • Maximum Point – greatestvalue of the function

  9. Domain & Range • Domain – all x-values of a function • Range – all y-values of a function

  10. Notation • Interval – represents an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included • Set– using inequalities to describe the values

  11. Asymptote A line that a graph gets closer and closer to, but never crosses or touches

  12. Characteristics • Domain: • Range: • Intercepts: • Increasing or Decreasing? • Maximum or Minimum?

  13. Characteristics • Domain: • Range: • Intercepts: • Increasing or Decreasing? • Maximum or Minimum?

  14. Characteristics • Domain: • Range: • Intercepts: • Increasing or Decreasing? • Maximum or Minimum? • Horizontal Asymptote:

  15. Characteristics • Domain: • Range: • Intercepts: • Increasing or Decreasing? • Maximum or Minimum? • Horizontal Asymptote:

  16. Classwork Characteristics of Functions Worksheet 5 problems

  17. Homework Characteristics of Functions Worksheet 6 problems

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