Question
The graph shows the function f(x)=|x|+2 . Place the appropriate symbols in the equation of g(x) so that g(x) is a transformation of f(x) that follows the rule rx−axis . (1 point) g(x)= |x| 2
Answers
GPT-4o mini
To transform the function \( f(x) = |x| + 2 \) to follow the rule \( g(x) = \text{reflection across the x-axis} \), you need to apply a reflection transformation to the function.
To reflect \( f(x) \) across the x-axis, you multiply the function by -1. Therefore, the appropriate transformation would be:
\[
g(x) = -(|x| + 2)
\]
This can be simplified to:
\[
g(x) = -|x| - 2
\]
So, the correct form of \( g(x) \) reflecting \( f(x) \) across the x-axis would be:
\[
g(x) = -|x| - 2
\]
If you were specifically looking for the expression of \( g(x) \) that has the structure given (with the placeholder), it would look like:
\[
g(x) = -|x| + (-2)
\]
where you are placing appropriate negative signs for the reflection and the shift downwards by 2 units.
To reflect \( f(x) \) across the x-axis, you multiply the function by -1. Therefore, the appropriate transformation would be:
\[
g(x) = -(|x| + 2)
\]
This can be simplified to:
\[
g(x) = -|x| - 2
\]
So, the correct form of \( g(x) \) reflecting \( f(x) \) across the x-axis would be:
\[
g(x) = -|x| - 2
\]
If you were specifically looking for the expression of \( g(x) \) that has the structure given (with the placeholder), it would look like:
\[
g(x) = -|x| + (-2)
\]
where you are placing appropriate negative signs for the reflection and the shift downwards by 2 units.