State the order and type of each transformation of the graph of the function ƒ(x) = –|(x + 6)| + 4 as compared to the graph of the base function.

a) left 6 units, up 4 units, reflection about the x-axis

b) left 6 units, reflection about the x-axis, up 4 units

c) right 6 units, up 4 units, reflection about the y-axis

d) left 6 units, reflection about the y-axis, up 4 units

A) left 6 units, up 4 units, reflection about the x-axis  

Step-by-step explanation:

The given absolute value function is

ƒ(x) = –|(x + 6)| + 4

The base function is

There is a transformation of the form;

The base function is shifted left 6 units. (+b means left shift) and shifted up 4 units (+4 means upward vertical shift), and reflected in the x-axis , (-g(x)) means reflection in the x-axis.

The correct choice is A.

A) left 6 units, up 4 units, reflection about the x-axis

Step-by-step explanation:

For absolute function , the parent function is

f(x) ---> f(x+a) , the graph will be shifted 'a' units to the left

6 is added with x so, we move graph 6 units left.

f(x) ---> f(x)+a , the graph will be shifted 'a' units up

4 is added with x. So, we move graph 4 units up

f(x) ---> -f(x) , the graph will be reflected over x-axis

we have negative sign in the front of the equation, so there will be a reflection about the x-axis

The order of transformation is

moving left 6 units, moving up by 4 units and a reflection about x-axis

answer: 1722

step-by-step explanation:

given: the mass of saturn=

the mass of mercury=

the number of times the mass of saturn is greater than the mass of mercury

hence, the mass of saturn is 1722 times greater than the mass of mercury.