How do you graph #y = x - |x|#?

Answer 1

See graph and explanation.

Partially,

#x - abs x = x - x = 0, x >=0# and

= x - (-x) = 2x, x <= 0#.

So, the graph is the radial line from O in #Q_3# that is truncated
from y = 2x and x-axis, #x>=0#. See the obtuse-angle graph.

graph{y-x+abs x=0}

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Answer 2

To graph ( y = x - |x| ), follow these steps:

  1. Identify critical points where the expression inside the absolute value function changes sign.
  2. Create a table of values by choosing x-values around these critical points.
  3. Plug each x-value into the equation ( y = x - |x| ) to find the corresponding y-values.
  4. 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.

Graph of y = x - |x|

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Answer from HIX Tutor

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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