# Given the piecewise function #f(x) = {2x + 1,x < -3 and 4x + 1, x ≥ -3}#, how do you evaluate f(-3)?

To evaluate ( f(-3) ), we need to check which part of the piecewise function applies to the value ( x = -3 ). In this case, the second part ( 4x + 1 ) applies when ( x ) is greater than or equal to ( -3 ). Therefore, we use the expression ( 4x + 1 ) to find ( f(-3) ). Substituting ( x = -3 ) into the expression, we get:

[ f(-3) = 4(-3) + 1 = -12 + 1 = -11 ]

So, ( f(-3) = -11 ).

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From the definition of the function you have

hence substitute the value to the function you get

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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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