# How do you find the vertex, and tell whether the graph #y = 14 - 7/5 abs(x - 7)# is wider or narrower than #y=absx#?

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To find the vertex of the absolute value function ( y = |14 - \frac{7}{5} |x - 7| ):

- Set the expression inside the absolute value equal to 0 and solve for ( x ) to find the vertex's x-coordinate.
- Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the y-coordinate.

To determine whether the graph of ( y = 14 - \frac{7}{5} |x - 7| ) is wider or narrower than ( y = |x| ):

Compare the coefficient of ( x ) in both equations. If the absolute value of the coefficient of ( x ) in the absolute value function is less than 1, the graph is wider than the standard absolute value function. If it is greater than 1, the graph is narrower.

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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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