Answer:
The correct answer to given question is option (a).
Step-by-step explanation:
Given function: f(x)= -2|x+1|
we need to put random values of x in given function to see that range of the given function f(x) is all real numbers.
when:
x=0; f(0)= -2|0+1|= -2|1|= -2
when x is positive i.e. x>0
x=1; f(1)= -2|1+1|= -2|2|= -4
x=2; f(2)= -2|2+2|= -2|4|= -8
when x is negative i.e. x<0
x= -1; f(-1)= -2|-1+1|= -2|0| =0
x=-2; f(-2)= -2|-2+1|= -2|-1|=2 (with the help of mod property |-1|=1)
hence, we saw that
when we take x>0; f(x)<0
when x<0; f(x)>0
we can conclude from above steps that the range of function f(x)= -2|x+1| is all real numbers.
