Select all the correct answers.

consider the following graph of function f.

which transformations will change function f into function g given below.

g = |x = 4| - 4

a vertical shift down 3 units

a vertical shift down 5 units

a horizontal shift left 4 units

a horizontal shift right 7 units

a horizontal shift left 7 units

a vertical shift up 5 units

answer:

b and e

step-by-step explanation:

the graphs equation is f=i x-3 i +1. you have to get from that to g=i x=4 i -4.

simple, difference from -3 to 4 is 7. in this spot is the left or right option.

since the difference is positive it goes left. (e)

then the difference from +1 to -4 is -5. in this spot   its the up or down option so since the difference is negative it goes down. (b)

We have that the function f has its minimum of 1 at the point 3. so it is of the form |x-3|+1 since it has the shape of an absolute value function. we then have that if we want our function to become |x+4|-4, the change in the vertical axis will be a shift by )=5 units in total. it also needs to be downwards since it is reduced.
as far as the horizontal shift is regarded, the corner of the graph needs to move from x=3 to x=-4. hence, the shift has to be by 7 units to the left.
the correct choices are b and e.