hkrana1
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Rewrite without absolute value sign for different values of x.
y=-|2x+5|-|2x–5|
If x<-2.5
if x>2.5
if -2.53632.5

Respuesta :

Answer:

I know the second and third answers. The second is -10 and the third is -4x.

Step-by-step explanation:

For the given expression, when x<-2.5 , y = 4x; when x>2.5, y = -4x & when -2.5 < x < 2.5; y = 10.

Absolute Function:

  • These are the function having a range as non-negative values.
    (R ≥ 0 )
  • They are represented as y = | f(x) |.

How to solve the given question?

  1. Case 1: If x < -2.5:
    As x < -2.5, (2x + 5) < 0 ⇒ It will opened with ' - ' sign.
    As x < -2.5, (2x - 5) < 0 ⇒ It will opened with ' - ' sign.
    ∴ y = - {-(2x-5)} - {-(2x+5)}
    ∴ y = (2x-5)+(2x+5)
    ∴ y = 4x
  2. Case 2: If x > 2.5:
    As x > 2.5, (2x + 5) > 0 ⇒ It will opened with ' + ' sign.
    As x > 2.5, (2x - 5) > 0 ⇒ It will opened with ' + ' sign.
    ∴ y = - {(2x-5)} - {(2x+5)}
    ∴ y = -2x+5-2x-5
    ∴ y = -4x
  3. Case 3: -2.5 < x < 2.5
    As -2.5 < x < 2.5, (2x + 5) > 0 ⇒ It will opened with ' + ' sign.
    As -2.5 < x < 2.5, (2x - 5) < 0 ⇒ It will opened with ' - ' sign.
    ∴ y = - {(2x-5)} - {-(2x+5)}
    ∴ y = -2x + 5 + 2x + 5
    ∴ y = 10

Thus, when x<-2.5 , y = 4x; when x>2.5, y = -4x & when -2.5<x<2.5;y=10.

Learn more about Absolute Function here:

https://brainly.com/question/2473412

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