Answer: D.
Step-by-step explanation:
The equation [tex]f(x) = (x-1)^{2} - 2[/tex] works only for option D. If x is 2, for example, the equation would look like this: [tex]f(2) = (2-1)^{2} - 2[/tex]. This equals [tex](1)^{2} - 2[/tex] which equals negative one. Therefore, when x is 2, y is -1. All of the graphs have the point (2, -1). We can still tell though that it is not A or B because there are spaces in between the points. If x = 2.2, the equation would not work for A or B because there is not a point with an x value of 2.2. This is different for both C and D. Δ
Answer C ends off early. There are endpoints to the figure. If x = 4, the equation would not work. This is because there is no point in answer C that has an x value of 4. On the other hand, question D does have a point with an x value of 4.
If x = 4, the equation looks like [tex]f(4) = (4-1)^{2} - 2[/tex].
We can simplify this to [tex]f(4) = (3)^{2} - 2[/tex]
and then [tex]f(4) = 7[/tex]
This means that when x is 4, y is 7. This is true for no graph but option D. Therefore the answer to this problem is D.
