Question

How do you graph `y= -3 cos x+2`?

Answer 1

Start with the classic graph, `y=cosx`, then we can build up.

graph{cosx [-0.935, 6.86, -2.006, 1.89]}

Because the graph we want has a `-cosx`, we flip this graph about the `x`-axis, to get `y=-cosx`

graph{y=-cosx [-0.935, 6.86, -2.006, 1.89]}

We now want #y=-3cosx. This is a vertical stretch, scale factor 3.

graph{y=-3cosx [-4.413, 11.39, -3.66, 4.236]}

Finally, shift the graph up by 2 units to get our final graph, `y=-3cosx+2`

graph{-3cosx+2 [-4.413, 11.39, -3.66, 4.236]}