Question

Sketch a graph of the function f(x) = -3cos(x) + 1

Answer 1

To sketch the graph of the given function, notice that it is the result of applying some transformations to the parent function g(x)=cos(x).

Starting with the cosine parent function, apply a vertical stretch by 3 units:

$\cos (x)\rightarrow3\cos (x)$

Next, apply a reflection over the Y-axis:

$3\cos (x)\rightarrow-3\cos (x)$

Finally, apply a vertical translation by 1 unit up:

$-3\cos (x)\rightarrow-3\cos (x)+1$

Then, the graph of f(x)=-3cos(x)+1 is: