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Understanding Relations and Functions: Quadrants, Maps, and Tests

Learn about relations and functions through ordered pairs, table maps, and the vertical line test. Understand function rule tables to determine ranges for given domains.

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Understanding Relations and Functions: Quadrants, Maps, and Tests

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  1. Bell Ringer • What quadrant will you find the following points in: • (3, 2) • (-4, -9) • (123, -21.5) • (-98, -22) • (4892, -1) • (-974, 0) • (0, 0)

  2. Relations and Functions Mr. Haupt CC.2.4.8.B.2

  3. Relation • A relation is a set of ordered pairs. For example, the table below form a relation between age and height.

  4. Relations • You can list the set of ordered pairs in a relation using braces. • [(10, 4), (12, 4.5), (14, 5), (16, 5.5), (18, 6), (20, 6.2)] • These points can then be plotted on a graph to see how the values are related. Another way to look at it is using a table map…

  5. Table Maps • Back in Chapter 1, we learned that in order for a relation to be a function, there can only be exactly one output (range) for each input (domain). • List the domain and range values in order, and draw arrows from the domain to their range values.

  6. Example Table Map • Determine if this relation is a function: • [(11, -2), (12, -1), (13, -2), (20, 7)]

  7. Example 2 • Determine if the relation is a function: • [(-2, -1), (-1, 0), (6, 3), (-2, 1)]

  8. Vertical Line Test • An easy way to tell if a relation is a function is by using the vertical line test. • If you can draw a vertical line that touches two or more points on a line, it is not a function.

  9. Examples

  10. Examples

  11. Function Rule Tables • Function Rule Tables are simply plugging given values into a function to determine the range. • For example: • Evaluate the function rule f(a) = -3a + 5 for the domain {-3, 1, 4}

  12. Example 2 • Evaluate the function rule f(x) = x2 + 1 for the domain {-2, 0, 5}

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