Question

Use a vertical shift to graph the function. y = 2 + sin x

Answer 1

The first picture is correct.

A transformation like $f(x) \to f(x) + k$ results in a vertical shift of the function, k units up if k is positive, k units down if k is negative.

In this case, we're transforming $\sin(x) \to \sin(x) + 2$, so $k = 2$

So, the graph of this function is the graph of the sine function, shifted two units up. Needless to say, to solve this exercise you need to be familiar with the shape of the graph of the sine function, so that you can recognize it in its shifted versions.

So, for the sake of completeness:

- The first picture is the graph of the sine function, shifted two units up

- The second picture is the graph of the cosine function, shifted two units up

- The third picture is the graph of the sine function, shifted two units down

- The fourth picture is the graph of the cosine function, shifted two units down