Question

The graph of g(x) is a reflection and translation of f(x) = 2x Which equation represents g(x)?

Answer 1

Answer:

-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