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Which is the correct piecewise definition for the function |x−3|=y−1?

A. y=−x+2 for x≥−3 and y=x−4 for x<−3

B. y=x−2 for x≥3 and y=−x+4 for x<3

C. y=x−2 for x<3 and y=−x+4 for x≥3

D. y=−x+2 for x<−3 and y=x−4 for x≥−3

Respuesta :

sqdancefan

Answer:

B. y=x−2 for x≥3 and y=−x+4 for x<3

Explanation:

Answer choices B and C are the only ones with the breakpoint at x=3, where the absolute value function has an argument of zero.

Of those, answer choice B is the only one with a positive slope for x > 3, so is the only correct choice.

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lublana

Answer:

B.[tex]y= x-2\; for\; x\geq3\; and\; y=-x+4 \;for \;x<3[/tex]

Step-by-step explanation:

Given function

[tex]\mid{ x-3}\mid=y-1[/tex]

We know that the break of modulus function

f(x)=[tex]\mid{x-1} \mid[/tex]

f(x)

= x-1 for [tex]x\geq 1[/tex]

And [tex]f(x)=-(x-1)\; for\;x<1[/tex]

Therefore, similarly we break the modulus function in the same way

[tex]y-1=\mid{x-3}\mid[/tex]

we can write as

[tex]y-1= x-3 for\; x\geq3[/tex]

Therefore ,[tex]y=x-2 \;for\;x\geq 3[/tex] ( by using subtraction property of equality )

And [tex]y-1=-x+3\;for\;x<3[/tex]

We can write as [tex]y=-x+4 \;for\; x<3[/tex] (By simplication)

Hence, B.[tex]y=x-2\; for\; x\geq 3\; and \; y=-x+4\; for\; x<3[/tex] is correct option .

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