Question

What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

Answer 1

Answer: First Option

−2 • f(x)

Step-by-step explanation:

The function $y=log_2(x)$ passes through point (2,1) since the exponential function $2 ^ x = 2$ when $x = 1$.

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 $(x_0, y_0)$ belonged to f(x), then $(x_0, -2y_0)$ belongs to the transformed function. Therefore, if $f(x) = log_2 (x)$ 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:

$y = -2 * f (x)$

and the transformed function is:

$y = -2log_2 (x)$