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How do you write #y=|2x-4| # as a piecewise function?

Answer 1

Savannah Anderson

#y=2|x-2|>=0#.

#y =2(x-2), x >=2 and y=-2(x-2), x<=2#. See Socratic graph.

#y=2|x-2|>=0#.

#=2(x-2), x >=2 and#

#--2(x-2), x<=2#.

Graphically, the given equation represents the V-shaped

semi pair of lines

#(y^2--4(x-2)^2)=0#. The half that is off is below the point of

intersection (2, 0).

graph{2|x-2| [-10, 10, -5, 5]}

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Answer 2

Hazel Anglin

To write ( y = |2x - 4| ) as a piecewise function:

[ y = \begin{cases} 2x - 4 & \text{if } 2x - 4 \geq 0 \ -(2x - 4) & \text{if } 2x - 4 < 0 \end{cases} ]

So, the piecewise function representation of ( y = |2x - 4| ) is: [ y = \begin{cases} 2x - 4 & \text{if } x \geq 2 \ -(2x - 4) & \text{if } x < 2 \end{cases} ]

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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.