Answer :
To solve the problem of identifying the transformation described by the equation [tex]\( g(x) = (x - 3.2)^2 \)[/tex] from the original function [tex]\( f(x) = x^2 \)[/tex], we need to analyze how the graph of [tex]\( f(x) = x^2 \)[/tex] has been altered.
The general form of a horizontal shift in a function [tex]\( f(x) \)[/tex] is represented by [tex]\( f(x - h) \)[/tex], where [tex]\( h \)[/tex] is the amount and direction of the shift:
- If [tex]\( h \)[/tex] is positive, the graph shifts to the right by [tex]\( h \)[/tex] units.
- If [tex]\( h \)[/tex] is negative, the graph shifts to the left by [tex]\( |h| \)[/tex] units.
Given the function [tex]\( g(x) = (x - 3.2)^2 \)[/tex]:
- Here, [tex]\( h = 3.2 \)[/tex], which is a positive number.
- Therefore, the graph of [tex]\( f(x) = x^2 \)[/tex] is shifted to the right by [tex]\( 3.2 \)[/tex] units to create the graph of [tex]\( g(x) = (x - 3.2)^2 \)[/tex].
Thus, the correct description of the transformation is:
A. A horizontal shift to the right 3.2 units
The general form of a horizontal shift in a function [tex]\( f(x) \)[/tex] is represented by [tex]\( f(x - h) \)[/tex], where [tex]\( h \)[/tex] is the amount and direction of the shift:
- If [tex]\( h \)[/tex] is positive, the graph shifts to the right by [tex]\( h \)[/tex] units.
- If [tex]\( h \)[/tex] is negative, the graph shifts to the left by [tex]\( |h| \)[/tex] units.
Given the function [tex]\( g(x) = (x - 3.2)^2 \)[/tex]:
- Here, [tex]\( h = 3.2 \)[/tex], which is a positive number.
- Therefore, the graph of [tex]\( f(x) = x^2 \)[/tex] is shifted to the right by [tex]\( 3.2 \)[/tex] units to create the graph of [tex]\( g(x) = (x - 3.2)^2 \)[/tex].
Thus, the correct description of the transformation is:
A. A horizontal shift to the right 3.2 units
