Question

In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted

Answer 1

Answer:

Vertical shift is 2 units top and horizontal shift is $\frac{\pi }{2}$ units to the right

Step-by-step explanation:

Consider the function f(x) = a cos(bx + c) + d.

In this graph, the horizontal shift is -c/b and the vertical shift is d.

Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.

Here, a = -3, b = 2, c = -π and d = 2.

So, vertical shift = d = 2 units top and

horizontal shift = $-\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2}$ units to the right.