Answer:
false.
Step-by-step explanation:
Given the function g(x) = f(x − k), can be sketched f(x) shifted k units horizontally. if k is negative, the function is shifted k units to the left.
Given the function g(x) = f(x) + k, we can say that the function is translated vertically upwards k times. If k is negative, the function is translated vertically downwards k times.
In this case, the function is translated two units to the right and 3 units down because the number "-3" is negative.
So it's false. The graph is translated three units downwards and 2 units to the right.
The given statement is a false statement.
We know that the transformation of the type:
f(x) to f(x+k)
is a horizontal shift of the graph.
The graph is shifted k units to the right if k is negative and if k is positive then the graph is shifted k units to the left.
Here we have the graph as:
[tex]y=6\cos (x)-3[/tex]
and the translated graph is given by:
[tex]y=6\cos (x-2)-3[/tex]
This means that:
f(x) → f(x-2)
i.e. the graph is shifted horizontally 2 units to the right ( since k=2 is positive )
