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

So 4th choice seems more accurate than others.

Step-by-step explanation:

Given function is

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.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3