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?(1 point)

Two parabolas drawn on coordinate plane. X-axis range from negative 9 to 4 and y-axis range from negative 1 to 9 in unit increment.
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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.

Two lines drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
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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.

Two lines drawn on coordinate plane. X-axis range from negative 3 to 9 and y-axis range from negative 3 to 3 in unit increment.
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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.

Two curves drawn on coordinate plane. Both axes range from negative 5 to 5 in unit increment.
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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.

Answer 1

None of them.

Checking the horizontal shifts (compare a clear feature on each dotted graph with the matching feature on the solid graph):

- Graph 1 (parabolas): solid peak at x = −5, dotted peak at x = 0 → shift = −5 (left 5).
- Graph 2 (lines): x-values match → shift = 0.
- Graph 3 (lines): x-values match → shift = 0.
- Graph 4 (curves): solid features at x = 1.3, 0, −1.3 vs dotted at x = 3.3, 2, 0.7 → shift = −2 (left 2).

y = f(x−3) would be a right shift of 3 units (solid should be dotted shifted right 3). None of these graphs shows a right shift of exactly 3.