# How do you graph #y = |x| + 3 #?

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graph{abs(x)+3 [-10., 10, -1.5, 15]}

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To graph the equation (y = |x| + 3), we can start by recognizing that (|x|) represents the absolute value of (x), which means it will always be non-negative. So, (y) will be equal to (x) plus a constant value of 3.

To graph this equation, we can plot points on the coordinate plane. For (x < 0), the absolute value of (x) will be equal to (-x). For (x \geq 0), the absolute value of (x) will be equal to (x).

We can choose some values for (x) and find corresponding values for (y) to plot the points. For example, when (x = -2), (y = |-2| + 3 = 2 + 3 = 5). So, we have the point ((-2, 5)). Similarly, when (x = 0), (y = |0| + 3 = 0 + 3 = 3), giving us the point ((0, 3)). When (x = 2), (y = |2| + 3 = 2 + 3 = 5), resulting in the point ((2, 5)).

Plotting these points and recognizing that the graph forms a V-shape with the vertex at the point ((0, 3)), we can draw the graph accordingly. The graph will consist of two straight lines, one with a positive slope on the right side of the y-axis and one with a negative slope on the left side of the y-axis, meeting at the vertex ((0, 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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