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5. What is the solution to the system of equations y = 3x - 2 and y = g(x) where g(x) is defined by the function below?
First of all, this is an odd question. Three of the answers make no sense at all. It is plain to see that neither (0, -2) nor (1, 6) are points on g(x), the parabola shown.
Second, it is quite plain that (1, 1) is on that line, and that (1) = 3(1) - 2, so it fits the other equation in the system as well. The choice is (4).
Just to be thorough, how do we know that (6, 16) is a solution to g(x)?
You can see that g(x) has points (0, 4), (1, 1) and (2, 0), which is the vertex. This makes (3, 1) and (5, 4) points by reflection over the line of symmetry, if you couldn't tell from the graph. The parent function is x2 and it has been shifted two spaces to the right.
This means that g(x) = (x - 2)2.
Then g(6) = (6 - 2)2 = 16 and (16) = 3(6) - 2.
6. Which statement about statistical analysis is false?
(3) Observational studies can determine cause and effect relationships.
Experiments do that, not observational studies.
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