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Answer:
The first option:
Down 5, left pi/2.
Step-by-step explanation:
Let's define the translations in a general way.
Horizontal shift.
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x + N)
if N is positive, the shift is to the left.
if N is negative, the shift is to the right.
Vertical shift.
For a function f(x), a horizontal shift of N units is written as:
g(x) = f(x) + N
If N is positive, the shift is upwards.
If N is negative, the shift is downwards.
In this case, we have the function:
f(x) = 6*Sin(2*x + π) - 5
Where the original function was something like:
h(x) = 6*sin(2*x)
Here we can already see the vertical shift is of minus 5 units, so the shift is 5 units down.
then we get:
f(x) = h(x) - 5 = 6*sin(2*x) - 5
Now we can apply a shift to the left of π/2 units, so we get:
f(x) = h( x + π/2) - 5 = 6*sin(2*(x +π/2) ) - 5
f(x) = 6*sin(2*x +π ) - 5
Then the correct option is:
Down 5, left pi over 2