A coordinate plane's x-axis ranges from negative 9 to 9 and its y-axis ranges from negative 11 to 11, both by 1-unit increments. A concave up parabola labeled f of x equals x squared is plotted passing through 7 marked points. A parabola that opens upward and seven labeled points on the parabola are plotted on a coordinate plane. The parabola has bidirectional arrows and is labeled f left parenthesis x right parenthesis equals x squared baseline minus 3.
The image shows a parent function f(x)=x2
and a translated form f(x)=x2−3
. Which statement best describes this translation?
(1 point)
Responses
The function shifted vertically down 3 units and is wider than the original.
The function shifted vertically down 3 units and is wider than the original.
The parent function shifted horizontally to the right 3 units and did not change in any other way.
The parent function shifted horizontally to the right 3 units and did not change in any other way.
The function shifted horizontally to the right 3 units and is narrower than the original.
The function shifted horizontally to the right 3 units and is narrower than the original.
The parent function shifted vertically down 3 units and did not change in any other way.
1 answer
The correct response is:
The parent function shifted vertically down 3 units and did not change in any other way.
This is because the function \( f(x) = x^2 - 3 \) represents a vertical translation of the parent function \( f(x) = x^2 \) downward by 3 units. There are no changes in width or horizontal shifts in this transformation.
