How do you graph #y = -abs(x+10)#?

Answer 1

First, lets remember the absolute value operator:

#AAc in RR# (for every element #c# in the real numbers set)
#if c>=0, abs(c) = c#
#if c<0, abs(c) = -c#
When graphing an absolute value operator, there are actually #2# graphs. Because the absolute value operation behaves in #2# different ways related to its input.
So we need to find the critical point of the absolute value. This means, we need to find the exact value of #x# where the greater values will result the output as is and the smaller values will result the output as negated.
Now it is obvious that #0# is the critical point of the absolute value operation.

To find the critical point in this problem:

#x+10=0#
#x=-10#
When #x# is greater than #-10# the input will be positive. When smaller, it will be negative.

Now we are ready to graph the line.

When #x>=-10#, #y = - (x+10) = -x - 10#
When #x<-10#, #y = - (-1) * (x+10) = x + 10#

The graph will look like this:

graph{y = - abs(x+10) [-20, 10, -5, 5]}

Why there is no positive #y#? Remember the conditions while graphing the lines. (#x>=10# and #x<-10#) When you try to plug some values of #x# you will see that there is no chance for #y# to be positive.
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Answer 2

To graph ( y = -|x + 10| ), follow these steps:

  1. Identify the vertex of the absolute value function, which is at the point (-10, 0).
  2. Plot the vertex on the coordinate plane.
  3. Since the coefficient of ( x ) is negative, the graph will open downwards.
  4. Determine the points to the left and right of the vertex.
  5. Plot these points symmetrically around the vertex.
  6. Connect the points with a smooth curve.

The resulting graph will be a downward-facing V-shape with the vertex at (-10, 0).

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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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