Answer: First Option
−2 • f(x)
Step-by-step explanation:
The function [tex]y=log_2(x)[/tex] passes through point (2,1) since the exponential function [tex]2 ^ x = 2[/tex] when [tex]x = 1[/tex].
Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair [tex](x_0, y_0)[/tex] belonged to f(x), then [tex](x_0, -2y_0)[/tex] belongs to the transformed function. Therefore, if [tex]f(x) = log_2 (x)[/tex] passed through point (2, 1) then the transformed function passes through point (2, -2)
The transformation that multiplies to f(x) by a factor of -2 is:
[tex]y = -2 * f (x)[/tex]
and the transformed function is:
[tex]y = -2log_2 (x)[/tex]
