Graph Transformations

Question

 (a) The graph of y=f(x+4) is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(b) The graph of y=f(x)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(c) The graph of y=f(x−5)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

(d) The graph of  y=f(x+5)−1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ?

Answer 1

Inside the parenthesis is a horizontal shift. The direction is the opposite of what you would think. + is to the left and - is to the right. Outside the parenthesis is vertical. + is up and - is down. 

(a) The graph of y=f(x+4) is the graph of y=f(x)

shifted horizontally ? and shifted vertically ? Horizontal to the left 4 units.

(b) The graph of y=f(x)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ? Vertically up one unit

(c) The graph of y=f(x−5)+1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ? Horizontally right 5 units and vertically up one unit.

(d) The graph of  y=f(x+5)−1 is the graph of y=f(x)

shifted horizontally ? and shifted vertically ? Horizontally left 5 units and vertically down one unit.

Answer 2

 (a) The graph of y=f(x+4) is the graph of y=f(x)

shifted vertically ? up 4 units

(b) The graph of y=f(x)+1 is the graph of y=f(x)

shifted horizontally ? -1 unit left

(c) The graph of y=f(x−5)+1 is the graph of y=f(x)

shifted horizontally ? -1 units left and shifted vertically ? down 5 units

(d) The graph of  y=f(x+5)−1 is the graph of y=f(x)

shifted horizontally ? right 1 unit and shifted vertically ? up 5 units