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masha68 [24]
3 years ago
11

How can you determine if a piece-wise relation is a function?

Mathematics
1 answer:
uysha [10]3 years ago
7 0
Use the vertical line rule to test. 
Imagine you are drawing lines parallel to the y axis, if any of your lines touches the graph twice, the graph does not represent a function. otherwise, it does. 
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(5x+6x)+(3y+9y)

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\huge\boxed{\bf\:1}

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\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }

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Now factorise the next set : \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }.

\frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\=  \frac{x-4}{x-1}

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\frac{ x  ^ { 2  }  -4x+3  }{ x  ^ { 2  }  -7x+12  }   \times   \frac{ x  ^ { 2  }  +2x-24  }{ x  ^ { 2  }  +5x-6  }    ^ {   }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}

\rule{150pt}{2pt}

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