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

9.55 degrees.

step-by-step explanation:

the given angle is

1 cycle is equal to 2π radians. so 4π will be equal to two cycles.

5.166667π-4π = 1.166667π

hence, this angle goes a little more than negative x axis.

1.166667π-π= 0.166667π

hence, the reference angle is 0.166667π radians.

1 radian = 57.2958 degrees

now, in degrees, this should be equals to 9.55 degrees.

0.85 or 85%

step-by-step explanation:

1) divide 23 by 27

2) round the decimal to the nearest 10

3) so your answer would be 0.85 or 85%