How do you write #f(x) = 2x+3# as a piecewise function?
Use the definition:
Using the definition:
It is good practice to simplify the inequalities:
Finished:
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To write the function ( f(x) = 2x + 3 ) as a piecewise function, you consider two cases: when ( 2x + 3 ) is nonnegative and when it is negative.

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

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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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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