What kind of transformation converts the graph of f(x) = 9(x - 2)^2 - 5 into the graph of g(x) = 9(x - 2)^2 - 9? Choices: (A)translation 4 units down (B)translation 4 units right (C)translation 4 units up (D)translation 4 units left

Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x) = 9(x - 2)^2 - 5 and g(x) = 9(x - 2)^2 - 9. Both functions have the same squared term 9(x - 2)^2, which means the parabolas they represent have the same shape and orientation. The only difference is in the constant term at the end of each function. This indicates a vertical shift.Vertical Shift Direction: Determine the direction of the vertical shift. The constant term in f(x) is -5, and in g(x) it is -9. Since -9 is less than -5, the graph of g(x) is shifted down relative to the graph of f(x).Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference between the constant terms is -9 - (-5) = -9 + 5 = -4. This means the graph of g(x) is shifted 4 units down from the graph of f(x).

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What kind of transformation converts the graph of $f(x) = 9(x - 2)^2 - 5$ into the graph of $g(x) = 9(x - 2)^2 - 9$ ? $\newline$ Choices: $\newline$ (A) translation $4$ units down $\newline$ (B) translation $4$ units right $\newline$ (C) translation $4$ units up $\newline$ (D) translation $4$ units left

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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) = 9(x - 2)^2 - 5

into the graph of

g(x) = 9(x - 2)^2 - 9

\newline

Choices:

\newline

(A) translation

4

units down

\newline

(B) translation

4

units right

\newline

4

units up

\newline

(D) translation

4

units left

Analyze Functions: Analyze the given functions to determine the type of transformation. We have $f(x) = 9(x - 2)^2 - 5$ and $g(x) = 9(x - 2)^2 - 9$ . Both functions have the same squared term $9(x - 2)^2$ , which means the parabolas they represent have the same shape and orientation. The only difference is in the constant term at the end of each function. This indicates a vertical shift.
Vertical Shift Direction: Determine the direction of the vertical shift. $\newline$ The constant term in $f(x)$ is $-5$ , and in $g(x)$ it is $-9$ . Since $-9$ is less than $-5$ , the graph of $g(x)$ is shifted down relative to the graph of $f(x)$ .
Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference between the constant terms is $-9 - (-5) = -9 + 5 = -4$ . This means the graph of $g(x)$ is shifted $4$ units down from the graph of $f(x)$ .