Question

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

logarithmic graph passing through point 2, negative 2.

−2 • f(x)
2 • f(x)
f(x) − 2
f(x) + 2

Answer 1

Answer: First Option

−2 • f(x)

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)`