Question

What is the range of the function f(x)=-2|x+1|?

Answer 1

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.

Answer 2

Answer:

A. all real numbers