suppose the graph of ( f ) is given. describe how the graph of each function can be obtained from the graph…

suppose the graph of ( f ) is given. describe how the graph of each function can be obtained from the graph of ( f ).\n(a) ( y = f(x + 5)+2 )\nshift 2 units to the right and 5 units upward\nshift 2 units to the right and 5 units downward\nshift 5 units to the left and 2 units downward\nshift 5 units to the right and 2 units upward\nshift 5 units to the left and 2 units upward\n(b) ( y = f(x - 4)-3 )\nshift 4 units to the right and 3 units downward\nshift 3 units to the left and 4 units upward\nshift 3 units to the right and 4 units downward\nshift 4 units to the right and 3 units upward\nshift 4 units to the left and 3 units downward

suppose the graph of ( f ) is given. describe how the graph of each function can be obtained from the graph of ( f ).\n(a) ( y = f(x + 5)+2 )\nshift 2 units to the right and 5 units upward\nshift 2 units to the right and 5 units downward\nshift 5 units to the left and 2 units downward\nshift 5 units to the right and 2 units upward\nshift 5 units to the left and 2 units upward\n(b) ( y = f(x - 4)-3 )\nshift 4 units to the right and 3 units downward\nshift 3 units to the left and 4 units upward\nshift 3 units to the right and 4 units downward\nshift 4 units to the right and 3 units upward\nshift 4 units to the left and 3 units downward

Answer

Brief Explanations:

For part (a), when we have a function (y = f(x + 5)+2), according to the rules of function transformations:

  • For the horizontal transformation, if we have (y = f(x + h)) ((h>0)), the graph of (y = f(x)) is shifted (h) units to the left. Here (h = 5), so there is a shift of 5 units to the left.
  • For the vertical transformation, if we have (y=f(x)+k) ((k > 0)), the graph of (y = f(x)) is shifted (k) units upward. Here (k = 2), so there is a shift of 2 units upward.

For part (b), when we have a function (y = f(x - 4)-3), according to the rules of function transformations:

  • For the horizontal transformation, if we have (y = f(x - h)) ((h>0)), the graph of (y = f(x)) is shifted (h) units to the right. Here (h = 4), so there is a shift of 4 units to the right.
  • For the vertical transformation, if we have (y=f(x)+k) ((k<0)), the graph of (y = f(x)) is shifted (|k|) units downward. Here (k=- 3), so there is a shift of 3 units downward.

Answer:

(a) shift 5 units to the left and 2 units upward (b) shift 4 units to the right and 3 units downward