Answer:
Range all real numbers less than or equal to 0
( - ∞ , 0 ]
Step-by-step explanation:
For visual understanding a graph of the function is attached with the answer.
- For calculating the range of any modulus function you need to know that if modulus is there across any function then the output will be always positive.
For example: x has a range of ( - ∞ , + ∞ ) but |x| has a range of [ 0 , + ∞ ). Similarly range of |x + 1| is [ 0 , + ∞ ).
- If you multiply the modulus function with a negative sign then the output will always be negative.
For example: Range of |x| is [ 0 , + ∞ ) but range of -|x| is ( - ∞ , 0 ]. Similarly range of -|x + 1| is ( - ∞ , 0 ]
- Range in this case won't be affected on multiplying a positive constant with the modulus function.
Therefore the range of f(x) = -2|x + 1| will be ( - ∞ , 0 ].
(NOTE : <em>[a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.</em>
<em>(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.</em>
<em>(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.</em>
<em>[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.</em>
<em>{a,b} means only 'a' and 'b'.</em>
<em>{a,b] or (a,b} doesn't mean anything.</em> )
