The point $( 3,9 )$ on the graph of $f ( x ) = x ^ { 2 }$ has been shifted to the point $( 4,7 )$ after a rigid transformation. Identify the shift and write the new function $g$ in terms of $f$ .
A)Shift: shifted 1 unit to the left. $h ( x ) = ( x + 1 ) ^ { 2 }$
B)Shift: horizontally 3 units to the left and vertically 2 units downward. $h ( x ) = ( x + 3 ) ^ { 2 } - 2$
C)Shift: horizontally 2 units to the right and vertically 1 unit upward. $h ( x ) = ( x - 2 ) ^ { 2 } + 1$
D)Shift: horizontally 1 unit to the right and vertically 2 units downward. $h ( x ) = ( x - 1 ) ^ { 2 } - 2$
E)Shift: shifted 1 unit upward. $h ( x ) = x ^ { 2 } + 1$

Question

Quizplus · Accepted Answer

The point $(3,9)$ has been moved to $(4,7)$, indicating a shift of 1 unit to the right (from $x = 3$ to $x = 4$) and 2 units downward (from $y = 9$ to $y = 7$). This corresponds to the transformation $g(x) = (x - 1)^2 - 2$, which is option D.

The Point (3,9)( 3,9 )(3,9) On the Graph Of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2

The Point $( 3,9 )$ On the Graph Of $f ( x ) = x ^ { 2 }$