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Understanding Functions: Definition, Graphs, and Domain & Range Concepts

This guide provides a thorough explanation of mathematical functions, emphasizing their definition and characteristics. A function is defined by the unique mapping of each member in the first set of data to one member in the second set, ensuring that for each input (x), there is a single output (y). We explore methods to identify functions through tables and graphs, highlighting the vertical line test for graph assessment. Additionally, we define domain and range, presenting examples to clarify how they are determined from given sets of values.

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Understanding Functions: Definition, Graphs, and Domain & Range Concepts

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Presentation Transcript

  1. Functions What’s a function and what can it look like? … Created by Rene’ McKibbin

  2. Function– each member of the first set of data is mapped to only one member of the second set of data – for every x there can only be one y

  3. Tables Function Function Not a Function

  4. Tables Not a Function Function

  5. MAPPINGs -6 -5 -4 -3 -2 0 1 5 6 9 11 15 15 10 7 0 1 2 3 4 Function Not a Function

  6. Graphs Note: If trying to determine if a graph is a function you must do the vertical line test, the line can only pass through the graph one time (red line) Not a Function Function Function

  7. Graphs Function Not a Function

  8. Domain & range • Domain – the set of all possible values that can be assigned to the independent variable in a function – your x value • Range – the set of all possible values of the dependent variable in a function – your y value Ex: (8,9), (-7,12), (0,5), (6,3) domain – {8, -7, 0, 6} or D: {-7 < x < 8} range – {9, 12, 5, 3} or R: {3 < y < 12}

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