The question asks about "these functions". In those circumstances would it be too much to expect that you make sure that there is something that these can refer to?
It is f(x) = -x^2.
In transformations a reflection across the x axis produces a mirror image
c
(2.5,-2.75)
reflection in the x-axis
It is f(x) = -x^2.
In transformations a reflection across the x axis produces a mirror image
For a reflection across the x axis, both the slope and the y intercept would have the same magnitude but the opposite sign.
y = -f(x) is a reflection of y = f(x) in the x axis.
c
(2.5,-2.75)
Reflection across the y-axis changes the sign of the x - coordinate only, that is, (x, y) becomes (-x, y).
A' = (-1, -2)
The reflection of a point across the y-axis involves changing the sign of the x-coordinate while keeping the y-coordinate the same. In this case, the point (-1, -5) will reflect to (1, -5) across the y-axis. This is because the x-coordinate changes from -1 to 1, while the y-coordinate remains -5.
reflection in the x-axis
Axial reflection is a type of transformation in geometry where a figure is reflected over an axis. The axis of reflection is a line that remains fixed while the rest of the figure is mirrored across it. This transformation preserves the size and shape of the figure.
f(x) = x + 1, to reflect this across the y-axis you need to reverse all the x values. Essentially, what this means is that, you rewrite f(x) as f(-x) making the function, -x + 1.