What kind of transformation converts the graph of f(x) = 10(x - 5)^2 + 10 into the graph of g(x) = 10(x - 5)^2? Choices: (A)translation 10 units down (B)translation 10 units left (C)translation 10 units right (D)translation 10 units up

Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x) = 10(x - 5)^2 + 10 and g(x) = 10(x - 5)^2. The only difference between f(x) and g(x) is the constant term at the end of the equation. This indicates a vertical shift.Vertical Shift Direction: Determine the direction of the vertical shift. Since f(x) has a +10 at the end and g(x) does not, this means that g(x) is f(x) shifted downwards by 10 units.Horizontal Shift Check: Confirm that the shift is not horizontal. There is no change in the (x - 5)^2 part of the function, which means there is no horizontal shift. The transformation is purely vertical.Conclusion: Conclude the type of transformation. The graph of f(x) has been shifted down by 10 units to obtain the graph of g(x). Therefore, the correct transformation is a translation 10 units down.

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What kind of transformation converts the graph of $f(x) = 10(x - 5)^2 + 10$ into the graph of $g(x) = 10(x - 5)^2$ ? $\newline$ Choices: $\newline$ (A) translation $10$ units down $\newline$ (B) translation $10$ units left $\newline$ (C) translation $10$ units right $\newline$ (D) translation $10$ units up

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Math Problems

Algebra 1

Describe function transformations

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Q. What kind of transformation converts the graph of

f(x) = 10(x - 5)^2 + 10

into the graph of

g(x) = 10(x - 5)^2

\newline

Choices:

\newline

(A) translation

10

units down

\newline

(B) translation

10

units left

\newline

10

units right

\newline

(D) translation

10

units up

Analyze Functions: Analyze the given functions to determine the type of transformation. We have $f(x) = 10(x - 5)^2 + 10$ and $g(x) = 10(x - 5)^2$ . The only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. This indicates a vertical shift.
Vertical Shift Direction: Determine the direction of the vertical shift. $\newline$ Since $f(x)$ has a $+10$ at the end and $g(x)$ does not, this means that $g(x)$ is $f(x)$ shifted downwards by $10$ units.
Horizontal Shift Check: Confirm that the shift is not horizontal. $\newline$ There is no change in the $(x - 5)^2$ part of the function, which means there is no horizontal shift. The transformation is purely vertical.
Conclusion: Conclude the type of transformation. $\newline$ The graph of $f(x)$ has been shifted down by $10$ units to obtain the graph of $g(x)$ . Therefore, the correct transformation is a translation $10$ units down.