Question

the graph of y= 6cos (x-2) - 3 is obtained by shifting the graph of y=6 cos x-3 horizontally 3 units to the right. true or false?

Answer 1

The given statement is a false statement.

Explanation:

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:

`y=6\cos (x)-3`

and the translated graph is given by:

`y=6\cos (x-2)-3`

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 )

Answer 2

false.

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.