Answer: D
Step-by-step explanation: This has to do with Transformations. With transformations, it follows this formula:
A (Bx±C) ± D
A is a vertical transformation where the graph is pulled upwards or squished downwards. If it is a whole number, like 2, the graph is pulled (stretched) up. If it is a fraction, like 1/2, the graph is squished.
B is a horizontal transformation where the graph is stretched outwards or squished inwards (think: accordian). If it is a whole number, like 2, the graph is squished inwards. If it is a fraction, like 1/2, the graph is stretched outwards.
C is a shift right or left. In this case, the ENTIRE graph moves right or left by C. If it is x+C, the graph moves left. If it is x-C, the graph moves right.
D is a shift up or down. In this case, the ENTIRE graph moves up or down by D. If it is +D, the grapjh moves up. If it is -D, the graph moves down.
If there are no Parenthesis or Square Root for B and C to be inside of, then there is no B and C. For the graph of x², for example, you might only have
Ax² ± D.
A graph of x² with parenthesis might look like this
A (Bx²± C) ± D.
Finally, if there is a negative (-) in front of A, that means the entire graph flips accross the x-axis, upsidown. If it is a parabola (x²), then the 'opening' or 'U-shape' faces down when there is a negative in front of A.
Ok, now that the basics are taken care of, we can analyze the graph provided. We are given with the basic graph of x². The first obvious noteicable thing we see is the fact that the new graph, g(x), has been moved down by 4 units.
We know that a shift Downwards is an effect of D, so we know the graph of g(x) looks like this so far:
x² - 4
However, that is not the only transformation that we can notice about g(x). We see that g(x) is flipped upsidown, with its 'U-shape' facing downwards. We know that this is because there is a negative in front of A.
So, g(x) looks like this now:
- x² - 4
After careful examination, there are no other noticeable transformations, so we figure out that g(x) = - x² - 4.
