When the equation f(x)=sin x is changed to g(x)=sin x−1, what impact does this have on the graph?

Question

Describe the key features that change (amplitude, period, or midline)

Choices:

1.  The graph has translated up 1 unit; the midline changes from y = 0 to y = 1 
2. The graph has translated down 1 unit; the midline changes from y=0 to y=−1
3. The graph has translated up 1 unit; the midline changes from y = 1 to y = 0
4. The graph has translated down 1 unit; the midline changes from y = -1 to y = 0 

Answer 1

I assume that the function g(x) = sin (x) - 1 not g(x) = sin (x - 1). All points of the parent function f(x) = sin (x) is translated 1 unit down and the midline from y=0 to y=-1. Amplitude and period have basically the same measure, just shifted. Second choice fits best the description.

Answer 2

The midline is an invisible line that cuts the graph in half. The midline equation is always y = d, where d is a number that added or subtracted on the outside of the function. In this case it starts at zero for the f(x) and then -1 for the g(x). So the answer is B.