Question

Which statement is true about f=(x)=-2/3|x+4|-6 ?

Answer 1

Answer:

The graph of f(x) has domain of x<=-6

Step-by-step explanation:

Given function is $f(x)=-\frac{2}{3}\left|x+4\right|-6$

compare this formula with f(x)=a|x-h|+k, we get h=-4, k=-6

We know that vertex for above formula is given by (h,k) then vertex for given function will be (-4,-6)

which is different than given choice so first choice is not possible.

We see that 2/3 is multiplied outside of the parent function |x| so that will create vertical not horizontal compress so 2nd choice is wrong.

when value of a is positive the graph opens up. But we have a=-2/3 which is negative so graph will open down. Hence 3rd choice is wrong.

Absolute function will have domain, all real number so x<=-6 is part of that which is partially correct.

So 4th choice seems more accurate than others.