Maria's Bike Journey Graph Analysis
Maria's bike journey graph depicts her distance from home as she rode to meet friends and run errands before returning home. The graph shows her stops for errands, changes in direction, and her path back home. By interpreting the key features of the graph, such as intercepts and intervals, we can analyze how Maria's journey unfolded.
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The graph below represents Marias 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. 1. What do the horizontal lines on the graph represent? 2. Where in the graph shows her taking care of the 2 errands? 3. Compare how she traveled at the beginning to how she traveled at the very end. 4. Create Maria s story so that it matches the graph.
MCC9-12.F.IF.4 (p. 51) For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior.
Characteristics of Functions
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)
Find the x and y intercepts, then graph. -3x + 2y = 12
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
Continuous vs Discrete Continuous has NO breaks Discrete has gaps or breaks
Extrema Maximum Point greatest value of the function Minimum Point least value of the function
Domain & Range Domain all x-values of a function Range all y-values of a function
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
Asymptote A line that a graph gets closer and closer to, but never crosses or touches
Characteristics 1. Domain: 2. Range: 3. Intercepts: 4. Increasing or Decreasing? 5. Maximum or Minimum?
Characteristics 1. Domain: 2. Range: 3. Intercepts: 4. Increasing or Decreasing? 5. Maximum or Minimum? 6. Horizontal Asymptote:
Classwork Characteristics of Functions Worksheet 5 problems
Homework Characteristics of Functions Worksheet 6 problems
