What kind of transformation converts the graph of f(x) = -10|x - 8| - 10 into the graph of g(x) = -10|x - 8| - 7? Choices: (A)translation 3 units up (B)translation 3 units left (C)translation 3 units down (D)translation 3 units right

Analyze Functions: Analyze the given functions to determine the type of transformation. We have f(x) = -10|x - 8| - 10 and g(x) = -10|x - 8| - 7. 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. The constant term in f(x) is -10, and in g(x) it is -7. Since -7 is greater than -10, the graph of g(x) is shifted up compared to the graph of f(x).Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference between the constant terms is -7 - (-10) = 3. This means the graph of g(x) is shifted 3 units up from the graph of f(x).

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What kind of transformation converts the graph of $f(x) = -10|x - 8| - 10$ into the graph of $g(x) = -10|x - 8| - 7$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units up $\newline$ (B) translation $3$ units left $\newline$ (C) translation $3$ units down $\newline$ (D) translation $3$ units right

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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 - 8| - 10

into the graph of

g(x) = -10|x - 8| - 7

\newline

Choices:

\newline

(A) translation

3

units up

\newline

(B) translation

3

units left

\newline

3

units down

\newline

(D) translation

3

units right

Analyze Functions: Analyze the given functions to determine the type of transformation. $\newline$ We have $f(x) = -10|x - 8| - 10$ and $g(x) = -10|x - 8| - 7$ . 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. The constant term in $f(x)$ is $-10$ , and in $g(x)$ it is $-7$ . Since $-7$ is greater than $-10$ , the graph of $g(x)$ is shifted up compared to the graph of $f(x)$ .
Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. The difference between the constant terms is $-7 - (-10) = 3$ . This means the graph of $g(x)$ is shifted $3$ units up from the graph of $f(x)$ .