## 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?

Question

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## Answers ( )

Answer:The given statement is a

false statement.Step-by-step 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:

and the translated graph is given by:

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: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.