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Find $g(x)$ , where $g(x)$ is the reflection across the x-axis of $f(x)=9|x+2|-4$ . $\newline$ Choices: $\newline$ $\text{}(A)g(x) = 9|x+2| - 4\text{]}$ $\newline$ $\text{}(B)g(x) = 9|x-2| - 4\text{]}$ $\newline$ $\text{}(C)g(x)=-9|x-2| +4\text{]}$ $\newline$ $\text{(D)}g(x) = -9|x + 2| + 4\text{]}$

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Reflections of functions

Full solution

Q. Find

g(x)

, where

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

.

\newline

Choices:

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

Multiply by $-1$ : To find the reflection of the function $f(x)$ across the $x$ -axis, we need to multiply the entire function by $-1$ . This will invert the graph of the function across the $x$ -axis.
Apply transformation: The original function is $f(x)=9|x+2|–4$ . To reflect this function across the x-axis, we will apply the transformation $g(x) = -f(x)$ .
Distribute negative sign: Applying the transformation to $f(x)$ , we get: $\newline$ $g(x) = -f(x)$ $\newline$ $g(x) = -(9|x+2|–4)$
Compare with choices: Distribute the negative sign through the function: $\newline$ $g(x) = -9|x+2| + 4$
Compare with choices: Distribute the negative sign through the function: $\newline$ g(x) = $-9|x+2| + 4$ Now we compare the result with the given choices to find the correct reflection of $f(x)$ across the $x$ -axis.

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