Question

Plz help me thank u math question
Which of the following expressions is equal to g(x)?

Answer 1

D. log (x-2)

Explanation:

We can see that in the graph of the function g(x), the graph is shifted toward the right.

We know that, to shift a graph to the right, we subtract that number of units inside the function.

For example if we are plotting a graph of F(x) and if we have to shift the function to the right by 2 units, we can write it as,
`F(x-2)`.

Similarly, here the graph of log (x) is shifted 2 units to the right so we can write the function as,

`log (x-2)` (we subtract inside the function).

Answer 2

D.
`log(x-2)`

Explanation:

We have been given function's
`f(x)=log(x)` graph and graph of function g(x). We are asked to choose the correct function formula for g(x).

We can see that our parent function f(x) is translated to right to get function g(x).

The rule for translating a function to right by k units is:

`f(x)\rightarrow f(x-k)`

We can see that our parent function is shifted 2 units to right as our parent function crosses x-axis at x equals 1, while our new function crosses x-axis at x equals 3. So our new function g(x) will be:

`g(x)=log(x-2)`

Therefore, the expression
`log(x-2)` is equal to g(x) and option D is the correct choice.