Let g(x) be the reflection of f(x)=3x+2 in the x axis. what is a function rule for G(x)
To reflect a function in the x-axis, we change the sign of the y-coordinates.
Since the function f(x) = 3x + 2 has a y-coordinate of 3x + 2, the reflection of this function in the x-axis, g(x), would have a y-coordinate of -3x - 2.
Therefore, the function rule for g(x) is g(x) = -3x - 2.
To find the function rule for g(x), the reflection of f(x)=3x+2 in the x-axis, we need to understand the effect of reflecting a function in the x-axis.
When a function is reflected in the x-axis, the y-values of the original function become their negatives. In other words, each point (x, y) on the graph of the original function f(x) will be reflected to the point (x, -y) on the graph of the reflected function g(x).
For the function f(x)=3x+2, when reflected in the x-axis, the negative of the y-value is taken. Thus, to obtain the function rule for g(x), we can simply change the coefficient of x from positive (+3) to negative (-3).
Therefore, the function rule for g(x), the reflection of f(x)=3x+2 in the x-axis, is:
g(x) = -3x + 2
To find the function rule for g(x), the reflection of f(x) across the x-axis, we can use the concept of reflection. When a function is reflected across the x-axis, the sign of the y-values is changed.
The function rule for f(x) is given as f(x) = 3x + 2. This means that for any x-value we input into the function, the output (y-value) is obtained by multiplying the x-value by 3 and then adding 2.
To reflect f(x) across the x-axis, we need to change the sign of the corresponding y-values. Thus, the function rule for g(x) is obtained by negating the expression for f(x).
As a result, the function rule for g(x) will be:
g(x) = -f(x)
Substituting the expression for f(x):
g(x) = -(3x + 2)
Therefore, the function rule for g(x) is g(x) = -3x - 2.