Respuesta :
Answer:
The required result is 5 unit vertically shifted downward and [tex]\frac{\pi}{2}[/tex] unit horizontally shifted left.
Step-by-step explanation:
Given : Graph [tex]f(x) = 6\sin(2x+\pi)-5[/tex]
To find : In what direction and by how many units is the graph vertically and horizontally shifted?
Solution :
Vertically shift is up or down,
Vertically shifting down is shifting outside the function,
i.e, f(x)→f(x)-b
In the given graph, The graph is 5 unit vertically shifted downward as
[tex]f(x) = 6\sin(2x+\pi)-5[/tex] i.e, 5 unit shifted downward.
Horizontal shift is either left or right,
Horizontally shift left is shifting inside the function,
i.e, f(x)→f(x+b)
We can write the given function as [tex]f(x) = 6\sin(x+\frac{\pi}{2})-5[/tex]
In the given graph, The graph is [tex]\frac{\pi}{2}[/tex] unit horizontally shifted left as
[tex]f(x) = 6\sin(x+\frac{\pi}{2})-5[/tex] i.e, [tex]\frac{\pi}{2}[/tex] unit shifted left.
Therefore, The required result is 5 unit vertically shifted downward and [tex]\frac{\pi}{2}[/tex] unit horizontally shifted left.
