How do you graph #y=x+42#?
The graph should look like this: graph{x+42 [10, 10, 5, 5]}
There is a way to mathematically calculate the different situations to graph this, but I will use the simpler way for this one.
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To graph the equation ( y = x + 4  2 ), follow these steps:

Identify the critical points where the absolute value expression inside the function changes sign. In this case, the critical point is when ( x + 4 = 0 ), which gives ( x = 4 ).

Plot the critical point ( (4, 2) ) on the graph. This point represents the vertex of the absolute value function.

Choose additional xvalues on either side of the critical point to determine the behavior of the absolute value function. For example, you can choose x = 5 and x = 3.

Substitute these xvalues into the absolute value function to find the corresponding yvalues. For x = 5, ( y = 5 + 4  2 = 1  2 = 1 ). For x = 3, ( y = 3 + 4  2 = 1  2 = 1 ).

Plot the points (5, 1) and (3, 1) on the graph.

Connect the plotted points using a straight line segment to represent the graph of the absolute value function.
The resulting graph will have a Vshape centered at the critical point (4, 2), with the vertex at that point and extending upwards.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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