Question

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.f(x) = -2(x + 1)2 + 2

Answer 1

Okay, here we have this:

Considering the provided function, we are going to graph it, so we obtain the following:

First, we are going to start with the graph of the basic function, so the graph so far is:

Now, we are going to add 1 inside the square, which is reflected in a shift of the graph one unit to the left, so we have:

We continue, multiplying the entire function by -2, which results in a compression of the graph, and in a reflection on the x-axis due to the change of sign, now we have:

And finally we add two units to the whole function, therefore it means that the graph will move up two units, leaving the following graph:

Finally we obtain that the correct answer is the first answer choice.