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How do you decide whether the relation #abs(x)-y=5# defines a function?

Answer 1

Nathan Axel

As #x# is the independent variable and any 1 value of #x# gives only 1 answer for #y# this is a function

This is called a one-to-one mapping

Make #x# the independent variable and #y# the dependent (the answer)

Add #y# to both sides

#|x|=5+y#

Subtract 5 from both sides

#y=|x|-5#

As #x# is the independent variable and any 1 value of #x# gives only 1 answer for #y# this is a function

This is called a one-to-one mapping

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Answer 2

Jace Anderson

To determine if the relation defines a function, we need to check if for every value of ( x ), there is exactly one corresponding value of ( y ). If we solve the relation for ( y ), we get ( y = |x| - 5 ). This relation passes the vertical line test, indicating that it defines a function. Therefore, the relation ( |x| - y = 5 ) does define a function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.