How do you graph #y = x - |x|#?
See graph and explanation.
Partially,
= x - (-x) = 2x, x <= 0#.
graph{y-x+abs x=0}
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To graph ( y = x - |x| ), follow these steps:
- Identify critical points where the expression inside the absolute value function changes sign.
- Create a table of values by choosing x-values around these critical points.
- Plug each x-value into the equation ( y = x - |x| ) to find the corresponding y-values.
- Plot the points on the coordinate plane and connect them to form the graph.
Here's the graph:
- For ( x < 0 ), ( y = x - (-x) = 2x ).
- For ( x \geq 0 ), ( y = x - x = 0 ).
So, the graph consists of two lines intersecting at the origin: one with a slope of 2 passing through the origin in the positive x-direction, and one horizontal line at y = 0 for non-positive x-values.
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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.
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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