Vertical line Test used in Function Algebra

Algebra 1

1. PRIMETIME Is the given relation below a function? Explain. {(0, 1), (2,4), (5,7), (3, 5) , ( 3, 6)} Answer: No. It is not a function. The x value 3 is assigned to 5 and 6.

2. Describe a functional relationship in terms of a rule which assigns to each input exactly one output. Learning Goals Determine whether a relation (represented as a mapping, set of ordered pairs, table, sequence, graph, equation, or context) is a function.

3. FILL IN THE BLANK A function is a relation which describes that there should be only one output for each __________. To identify a function from a relation, check to see if any of the ___________ values are repeated - if not, it is a function . input x

4. Activity 4 Functions as Graphs The vertical line test is a visual method used to determine whether a relation represented as a graph is a function. To apply the vertical line test, consider all of the vertical lines you can draw on the graph of a relation. When any vertical line intersects the graph at more than one point, the relation is not a function. Page 409

5. Activity 4 WORKED EXAMPLE Consider the scatter plot shown. In this scatter plot, the relation is not a function. The input value 4 maps to two different outputs, 1 and 4. Those two outputs intersect the vertical line drawn at x = 4. Page 409

6. Activity 4 Use the definition of function to explain why the vertical line test works. Look back at the graphs of the sequences in the lesson Patterns, Sequences, Rules .... Which sequences are functions? TAKE NOTE... Page 409

7. 2. Use the 12 cards that you sorted in the previous lesson. Sort the graphs into two groups: functions and non-functions. Use the letter of each graph to record your findings. Page 409 PAIRWORK 5 minutes

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9. 2. Use the 12 cards that you sorted in the previous lesson. Sort the graphs into two groups: functions and non-functions. Use the letter of each graph to record your findings. Page 409

10. Activity 5 Functions as Equations So far, you have determined whether a mapping, context, or a graph represents a function. You can also determine whether an equation is a function.

11. Activity 5 WORKED EXAMPLE You can use the equation y = 3 x to convert yards to feet. Let x represent the number of yards, and let y represent the number of feet. You can use the equation y = 3 x to convert yards to feet. Let x represent the number of yards, and let y represent the number of feet. To test whether this equation is a function, first, substitute values for x into the equation, and then determine whether any x -value maps to more than one y -value. When each x -value has exactly one y -value, it is a function. Otherwise, it is not a function. In this case, every x -value maps to only one y -value. You multiply each x -value by 3. Therefore, this equation is a function. Page 410

12. Activity 5 It is impossible to test every possible input value to determine whether or not the equation represents a function. You can graph any equation to see the pattern and use the vertical line test to determine whether it represents a function. Determine whether each equation is a function. List three ordered pairs that are solutions to each. Explain your reasoning. y = 5 x + 3 y = x 2 y = | x | x 2 + y 2 = 1 y = 4 x = 2 If you do not recognize the graph, use a graphing calculator to see the pattern. THINK ABOUT... PAIRWORK

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