# How do you write #y = |6 + 2x| + 1 # as a piecewise function?

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To write ( y = |6 + 2x| + 1 ) as a piecewise function, we can break it down based on the sign of the expression inside the absolute value:

[ y = \begin{cases} 6 + 2x + 1 & \text{if } 6 + 2x \geq 0 \ -(6 + 2x) + 1 & \text{if } 6 + 2x < 0 \end{cases} ]

Simplifying further:

[ y = \begin{cases} 2x + 7 & \text{if } x \geq -3 \ -2x + 7 & \text{if } x < -3 \end{cases} ]

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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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