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How do you write #p(x) = |x-1| +4# as a piecewise function?

Answer 1

Eli Assouline

Use the definition of the absolute value function:

#|a| = {(a; a >=0),(-a;a<0):}#

Given: #p(x) = |x-1| +4#

Please observe that #a = x-1# with regard to the definition:

#|x-1| = {(x-1; x-1 >=0),(1-x;x-1<0):}#

Simplify the inequalities

#|x-1| = {(x-1; x >=1),(1-x;x<1):}#

Add 4 to both sides:

#|x-1|+4 = {(x-1+4; x >=1),(1-x+4;x<1):}#

Simplify the right side and substitute #p(x)# on the left:

#p(x) = {(x+3; x >=1),(5-x;x<1):}#

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Answer 2

Isaiah Anthony

p(x) = |x - 1| + 4 can be expressed as a piecewise function as follows:

p(x) = { x - 1 + 4, if x ≥ 1 -(x - 1) + 4, if x < 1 }

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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.