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

question 85

Multiple Choice

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. \(h ( x ) = x ^ { 2 } + 1\)

---

Definitions:

Life-Span Development

The study of how individuals grow, change, and age throughout the course of their life, from conception to death.

Conception to Death

A phrase denoting the entire human life span, from the beginning of life at conception to its end at death.

Longitudinal Method

A research design that involves repeated observations of the same variables over short or long periods of time.

Developmental Psychology

Area of psychology in which the psychologists study the changes in the way people think, relate to others, and feel as they age.