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

Vertical shift is 2 units top and horizontal shift is
`(\pi )/(2)` units to the right

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 =
`-(c)/(b) =-(-\pi )/(2) =(\pi)/(2)` units to the right.