Find g(x), where g(x) is the reflection across the x-axis of f(x)=–3|x–3|+6.
Question
Find g(x), where g(x) is the reflection across the x-axis of f(x)=–3|x–3|+6.
Solution
To find the reflection of the function f(x) = -3|x-3|+6 across the x-axis, you simply need to change the sign of the function. This means that you multiply the entire function by -1.
So, the reflection of f(x) across the x-axis, which we'll call g(x), is:
g(x) = -1 * (-3|x-3|+6)
This simplifies to:
g(x) = 3|x-3|-6
So, g(x) = 3|x-3|-6 is the reflection of the function f(x) = -3|x-3|+6 across the x-axis.
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