Answered

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Which best describes the transformation from the graph of [tex][tex]$f(x)=x^2$[/tex][/tex] to the graph of [tex][tex]$f(x)=(x-3)^2-1$[/tex][/tex]?

A. Left 3 units, down 1 unit
B. Left 3 units, up 1 unit
C. Right 3 units, down 1 unit
D. Right 3 units, up 1 unit

Sagot :

GinnyAnswer
To describe the transformation from the graph of [tex]\( f(x) = x^2 \)[/tex] to the graph of [tex]\( f(x) = (x-3)^2 - 1 \)[/tex], we need to analyze the changes made to the function.

1. Horizontal Shift:
- The expression [tex]\( (x - 3) \)[/tex] inside the parentheses indicates a horizontal shift.
- If the term is [tex]\( (x - h) \)[/tex], the graph of the function shifts to the right by [tex]\( h \)[/tex] units. Here, [tex]\( h = 3 \)[/tex], so the graph shifts to the right by 3 units.

2. Vertical Shift:
- The expression [tex]\(-1\)[/tex] outside the parentheses indicates a vertical shift.
- If the term is [tex]\(- k\)[/tex] added or subtracted from the function, the graph shifts downward by [tex]\( k \)[/tex] units. Here, [tex]\( k = 1 \)[/tex], so the graph shifts downward by 1 unit.

Putting these two transformations together:
- The graph shifts 3 units to the right.
- The graph shifts 1 unit downward.

Hence, the best description of the transformation is:

right 3 units, down 1 unit
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