Question

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

Answer 1

Answer: Third option

$f(x) - 2$

Step-by-step explanation:

The function $y=log_3 (x)$ passes through the point (1,0) since the function $y=log_a (x)$ always cuts the x-axis at $x = 1$.

Then, if the transformed function passes through point (1,-2) then this means that the graph of $y=log_3(x)$ was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

$y = f (x) + k$

Where k is a negative number. In this case $k = -2$

Then the transformation is:

$f(x) -2$

and the transformed function is:

$y = log_3 (x) -2$