Question

Each of the function graphs represents an original function, marked by a dotted line graph, and a translated graph, marked by a solid line graph. Which graph shows that y=f(x−3)
is the result of the function y=f(x)
being translated by 3 units?



A. The solid line starts from left parenthesis negative 3 comma negative 1 right parenthesis and ends at left parenthesis 9 comma 3 right parenthesis. The dotted line starts from left parenthesis negative 3 comma 3 right parenthesis, and ends at left parenthesis 9 comma 1 right parenthesis.
B. The solid parabola starts from left parenthesis negative 8 comma 9 right parenthesis peaks down at left parenthesis negative 5 comma 0 right parenthesis ends at left parenthesis negative 2 comma 9 right parenthesis. The dotted parabola starts from left parenthesis negative 3 comma 9 right parenthesis peaks down at left parenthesis 0 comma 0 right parenthesis ends at left parenthesis 3 comma 9 right parenthesis.
C. The solid curve starts from left parenthesis 1.3 comma 5 right parenthesis, then touches origin and goes down to left parenthesis negative 1.3 comma 5 right parenthesis. The dotted curve starts from left parenthesis 3.3 comma 5 right parenthesis, then touches x-axis at 2 and goes down to left parenthesis 0.7 comma negative 5 right parenthesis.
D. The solid line starts from left parenthesis negative 5 comma 1.7 right parenthesis and ends at left parenthesis 5 comma 1.7 right parenthesis. The dotted line starts from left parenthesis negative 5 comma 2.7 right parenthesis, and ends at left parenthesis 5 comma 1.7 right parenthesis.

Answer 1

None of them.

Check the horizontal shifts of corresponding key points:
- A: corresponding x-values are the same (no horizontal shift).
- B: peak moves from x = 0 to x = −5 (shift left 5).
- C: x-intercept moves from x = 2 to x = 0 (shift left 2).
- D: x-values stay the same (a vertical shift).

None shows the solid graph = dotted graph shifted right by 3 (which is what y = f(x−3) represents).