Final answer:
g(x), the reflection of f(x) = 7x - 6 across the x-axis, is obtained by multiplying the y-values of f(x) by -1, resulting in g(x) = -7x + 6.
Step-by-step explanation:
To find g(x), the reflection of f(x) = 7x - 6 across the x-axis, each y-value of f(x) is multiplied by -1. This reflection changes the sign of the y-coordinate while leaving the x-coordinate unchanged. The reflected function g(x) would thus be g(x) = -f(x) = -(7x - 6) = -7x + 6.
Reflecting a graph across the x-axis essentially takes each point (x, y) on the original graph and transforms it to (x, -y). In this case, since the original function f(x) has a positive slope of 7, the reflected function g(x) will have a negative slope of -7. The y-intercept is also reflected, changing from -6 to +6 in g(x).