Question

Four transformations of the function f(x) are given below. For each transformation, drag the graph that shows the result of that transformation into the box under it.

Answer 1

g(x) = f(x) + 4 → Graph #5

h(x) = f(x + 4) → Graph #6

k(x) = f(x) - 4 → Graph #4

m(x) = f(x - 4) → Graph #3

Explanation:

g(x) = f(x) + 4 → Graph #5

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) up by 4.

⭐ Graph #5 exhibits this transformation because I took the point (0,1) and shifted it up 4 units to get (0,5). Graph #5 is the only graph that showed point (0,5).

h(x) = f(x + 4) → Graph #6

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the x-values of f(x) by -4.

⭐ Graph #6 exhibits this transformation because I took point (0,1) and shifted it left 4 units to get (-4,1). Graph #6 is the only graph that showed point (-4,1).

k(x) = f(x) - 4 → Graph #4

⭐ This transformation of f(x) means that to get g(x), you have to shift all of the y-values of f(x) down by 4.

⭐ Graph #4 exhibits this transformation because I took point (0,1) and shifted it down 4 units to get (0,-3). Graph #4 is the only graph that showed point (0,-3)

m(x) = f(x - 4) → Graph #3

⭐ This transformation of f(x) means that to get to g(x), you have to shift all of the x-values of f(x) right by +4.

⭐ Graph #3 exhibits this transformation because I took point (0,1) and shifted it right 4 units to get (4,1). Graph #3 is the only graph that showed point (4,1).