# How do you graph #f(x) =-3abs(x+2)+2#?

graph{-3|x+2|+2 [-11.24, 11.26, -5.625, 5.63]} f(x)=-3|x-2|+2=0 |x-2|=2/3 =>x-2=2/3, -(x-2)=2/3 x=8/3r x=4/3

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You can graph it step by step.

graph{|x + 2| [-4.093, 0.907, -0.41, 2.09]}

Finally, we have: graph{-3|x+2|+2 [-6.893, 3.107, -2.49, 2.51]}

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To graph the function ( f(x) = -3| x + 2 | + 2 ):

- Identify the vertex, direction, and stretch/compression factor.
- Plot the vertex on the coordinate plane.
- Use the stretch/compression factor to find additional points symmetrically around the vertex.
- Draw a smooth curve connecting the points to represent the graph.

Given that the absolute value function ( |x| ) reflects the negative values of ( x ) into positive, the vertex is at the point (-2, 2). Since the coefficient of ( x ) inside the absolute value function is -3, the graph is stretched by a factor of 3 vertically, and since it is negative, it opens downward.

Here's how to plot it:

- Plot the vertex at (-2, 2).
- Choose points symmetrically around the vertex. For example, when ( x = -3 ), ( |x + 2| = |-3 + 2| = |-1| = 1 ), so ( f(-3) = -3 \cdot 1 + 2 = -1 ).
- Another symmetric point could be when ( x = -1 ), which gives ( f(-1) = -3 \cdot 0 + 2 = 2 ).
- Connect the points with a smooth curve.

The graph of ( f(x) = -3| x + 2 | + 2 ) is a downward-facing V-shaped curve with its vertex at (-2, 2), stretched vertically by a factor of 3.

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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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