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Discrete and Continuous Functions: Graphs, Domain, and Range

Learn how to determine if a function is discrete or continuous, find the exact or reasonable domain and range, and analyze graphs. Examples provided.

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Discrete and Continuous Functions: Graphs, Domain, and Range

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  1. Pre-AP Algebra 2April 5, 2016 Goal(s): • Determine whether a given function is discrete or continuous • Determine the exact domain and range given a graph • Determine a reasonable domain and range from a problem situation

  2. Discrete and Continuous Functions Discrete Functions Continuous Functions Definition: the values belonging to the set include any values in the interval Examples: Height or weight of a person Time to complete a task Temperature or distance Graph: a series of connected points Generalization: discrete data is measured • Definition: the values belonging to the set are distinct and separate • Examples: • Number of people in a room • Number of coins in a drawer • Shoe sizes • Graph: a series of unconnected points • Generalization: discrete data is counted

  3. Example 1 Write and graph the function described below. Determine the domain and range. Spencer has up to 100 chocolate bars to sell for $2 each. The function f(x) gives the amount of money collected after selling x chocolate bars.

  4. Example 1 The graph consists of separate points, and it makes no sense to connect the points in this situation. Name the domain and range of the graph

  5. Example 2 Write and graph the function described below. Determine the domain and range. A low-flow shower head releases 1.8 gallons of water per minute. Katy typically showers for 10 minutes each morning. The function V(x) gives the volume of water released after x minutes.

  6. Example 2 The graph is an unbroken line or curve. It makes sense to connect the points in this situation. Name the domain and range of the graph

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