How do you write #f(x) = |2x+3|# as a piecewise function?

Answer 1

Use the definition:
#|f(x)| = {(f(x)", "f(x) >= 0),(-f(x)", "f(x) < 0):}#

Given #f(x) = |2x+3|#

Using the definition:

#f(x) = |2x+3| = {(2x+3", "2x+3 >= 0),(-2x-3", "2x+3 < 0):}#

It is good practice to simplify the inequalities:

#f(x) = {(2x+3", "2x >= -3),(-2x-3", "2x < -3):}#

Finished:

#f(x) = {(2x+3", "x >= -3/2),(-2x-3", "x < -3/2):}#
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Answer 2

To write the function ( f(x) = |2x + 3| ) as a piecewise function, you consider two cases: when ( 2x + 3 ) is non-negative and when it is negative.

  1. When ( 2x + 3 \geq 0 ): ( f(x) = 2x + 3 )

  2. When ( 2x + 3 < 0 ): ( f(x) = -(2x + 3) )

So, the piecewise function representation of ( f(x) = |2x + 3| ) is:

[ f(x) = \begin{cases} 2x + 3 & \text{if } 2x + 3 \geq 0 \ -(2x + 3) & \text{if } 2x + 3 < 0 \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.

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.

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.

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.

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