# P07 - x on the axes below Hint Use shifting reﬂecting etc...

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Project 7 MAC 2311 Throughout this assignment, we will refer to the following function: f ( x ) = - x + 4 x x - 2 - 8 x . 1. Write the domain of f ( x ). Rewrite f ( x ) as a simpliﬁed rational function in lowest terms. Include the restrictions on the domain. Using a number line, ﬁnd the intervals on which f ( x ) is positive and those intervals on which it is negative. This is a failsafe way to help to distinguish between limits that are or -∞ . Evaluate the following limits: lim x →- 2 - f ( x ) = lim x →- 2 + f ( x ) = lim x 0 - f ( x ) = lim x 0 + f ( x ) = lim x 4 - f ( x ) = lim x 4 + f ( x ) =

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Unformatted text preview: ( x ) on the axes below. Hint: Use shifting, reﬂecting, etc. along with the fact that x + b x + a = x + a x + a + b-a x + a = 1 + b-a x + a , to obtain your simpliﬁed function, and be mindful of your domain. .. 2. If possible, ﬁnd the value of the constant c so that lim x → 2 h ( x ) exists for the piecewise-deﬁned function below. h ( x ) = x 2-4 | x 2-2 x | x < 2 x + cx 2 x > 2 What is lim x → h ( x )?...
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P07 - x on the axes below Hint Use shifting reﬂecting etc...

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