Final answer:
To find the function g(x), the y-axis reflection of f(x), you use the transformation g(x) = f(-x). This changes the sign of the x coordinate, creating a mirror image over the y-axis, without affecting the y values.
Step-by-step explanation:
To find the function g(x), which is the reflection across the y-axis of the function f(x), you need to apply the concept of even and odd functions from the study of algebra.
A function reflected across the y-axis will have its x values negated, in other words, the reflection of f(x) across the y-axis is g(x) = f(-x). This transformation changes the sign of the x coordinate, thus mirroring the function over the y-axis.
As an example, if f(x) = x2 - 4x + 3, then the reflected function g(x) would be g(x) = f(-x) = (-x)2 - 4(-x) + 3 = x2 + 4x + 3.
Remember, even functions, which are symmetric about the y-axis, can be defined such that f(x) = f(-x), while odd functions (anti-symmetric about the origin) satisfy the property that f(x) = -f(-x).
Reflections do not apply to translations or functions concerning time (t), wave functions, gradients, or graphs of changing values that are not specifically about symmetry across axes.