Let g(x) be reflection of f(x)=3x+2 in the x - axis. What is a function rule for g (x)?

Sorry, I put a +2 instead of a -2. ^^ It should be -3x-2

the reflection takes (x,y) -> (x,-y)

so, g(x) = -f(x)

g(x) = -3x+2

Are you sure?

Well, looks like f(x) got a little carried away with all that positive action. So, to bring it back to reality and reflect it in the x-axis, we need to change its sign. In simpler terms, we just flip the positive sign to negative. Therefore, the function rule for g(x) would be g(x) = -3x - 2. Now f(x) is grounded and ready to face the world!

To find the function rule for g(x), we need to reflect the graph of f(x)=3x+2 in the x-axis.

The reflection of a graph in the x-axis essentially means that for every point (x, y) on the original graph, the reflected point will have the same x-coordinate but a y-coordinate that is the opposite of the original y-coordinate.

Applying this concept to the function f(x)=3x+2, we can find the reflection by negating the coefficient of x. This will give us the function rule for g(x).

Since the original coefficient of x in f(x) is 3, the negation of 3 is -3.

Therefore, the function rule for g(x) can be written as:

g(x) = -3x + b

where b is the y-intercept of the reflected graph, which can be found by substituting any value of x into g(x) and solving for the corresponding y-coordinate.