Let $$ g(x) $$ be the reflection of $$ f(x)=2 x+9 $$ in the $$ x $$-axis. What is a function rule for $$ g(x) $$ ? $$ \begin{array}{l}g(x)=-2 x+9 \ ext { o } g(x)=-2 x-9 \ g(x)=2 x+9 \ g(x)=2 x-9\end{array} $$

Question

Let $$ g(x) $$ be the reflection of $$ f(x)=2 x+9 $$ in the $$ x $$-axis. What is a function rule for $$ g(x) $$ ? $$ \begin{array}{l}g(x)=-2 x+9 \ 	ext { o } g(x)=-2 x-9 \ g(x)=2 x+9 \ g(x)=2 x-9\end{array} $$

UpStudy AI · Accepted Answer

$$ g(x) = -2x - 9 $$ To find the reflection of the function $$ f(x) = 2x + 9 $$ in the $$ x $$-axis, we need to negate the output of the function. This means that for any input $$ x $$, the output of the reflected function $$ g(x) $$ will be the negative of the output of $$ f(x) $$. The reflection in the $$ x $$-axis can be expressed mathematically as: $$ g(x) = -f(x) $$ Substituting $$ f(x) = 2x + 9 $$ into this equation gives: $$ g(x) = -(2x + 9) $$ Distributing the negative sign: $$ g(x) = -2x - 9 $$ Thus, the function rule for $$ g(x) $$ is: $$ g(x) = -2x - 9 $$ Therefore, the correct answer is: $$ g(x) = -2x - 9 $$

Let \( g(x) \) be the reflection of \( f(x)=2 x+9 \) in the \( x \)-axis. What is a function rule for \( g(x) \) ? \( \begin{array}{l}g(x)=-2 x+9 \\ \text { o } g(x)=-2 x-9 \\ g(x)=2 x+9 \\ g(x)=2 x-9\end{array} \)

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Let \( g(x) \) be the reflection of \( f(x)=2 x+9 \) in the \( x \)-axis. What is a function rule for \( g(x) \) ? \( \begin{array}{l}g(x)=-2 x+9 \\ \text { o } g(x)=-2 x-9 \\ g(x)=2 x+9 \\ g(x)=2 x-9\end{array} \)

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions