The graph of g (x) is a reflection and translation of f (x) = 2x

Which equation represents g (x) ?

-2x - 1 if f (x) is reflected along the x axis and translated 1 unit downward

Step-by-step explanation:

A function can either be reflected along the x axis or along the y axis. If a function is reflected along the x axis, the new reflected equation g (x) is given by:

g (x) = - f (x) = - 2x

g (x) = - 2x

If a function is reflected along the y axis, the new reflected equation g (x) is given by:

g (x) = f (-x) = 2 (-x)

g (x) = - 2x

Translation means the shifting of the curve either up or down in a graph. If the reflected function is shifted 1 unit upward, the function becomes:

g (x) + 1 = - 2x + 1

If the reflected function is shifted 1 unit downward, the function becomes:

g (x) - 1 = - 2x - 1