Question

Write y=2|x+2|−3 as a piecewise function.

Answer 1

Answer:

y = – 2x – 7 , if x < –2

= 2x + 1 , if x ≥ – 2

Point to be noted :

• A function can be written as piecewise function if it changes its behaviour ( increasing or decreasing ) about a point.

• The function f(x) = y = |x| changes its behaviour at |x| = 0 ie , x = 0 .

• y = | x | = x , if x < 0

= - x , if x > 0

• | x | = a => x = ± a

• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )

• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]

Solution:

Here,

The given function is : y = 2|x + 2| - 3

Here,

The function will change its behaviour when

=> | x + 2 | = 0

=> x + 2 = 0

=> x = -2

Now,

If x < -2 , then ;

=> y = 2[–(x +2)] – 3

=> y = –2x – 4 – 3

=> y = – 2x – 7

If x ≥ 2 , then ;

=> y = 2(x + 2) – 3

=> y = 2x + 4 – 3

=> y = 2x + 1

Hence ,

y = – 2x – 7 , if x < –2

= 2x + 1 , if x ≥ – 2