At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
The answer is really not that important. I really what to know what the expression is telling me.
|dw:1333271534128:dw| The graph is like this
the lowest point is -4
Range of f(x) means f(x) is between which two values from the graph, -4
i understand that, what about the....if x is =0 what does that mean and how does it effect the graph??
and whats with the 5 as well
as x=0, f(x) = 5 not 3x^2 -4. It reminds them to reject the value -4 at x=0 therefore, f(x) >-4 but not f(x) >= -4
|dw:1333276937858:dw|I look at the equation as that of a piecewise definition of a function. The second piece, y = 3 x^2 - 4 is one point short of being a parabola. Disallowing x = 0 from the domain of y = 3 x^2 - 4 has the effect of creating a hole where the point (0, -4) might have been. After drawing y = 3 x^2 -4 and placing a hole at (0, -4), go to the first piece of the definition of f(x). That is y = 5 when x = 0 which is the point (0,5). The graph of f(x) in its entirety is the union of the two pieces of the definition of f(x). That is a point graphed at (0, 5) and a discontinuous curve y = 3 x^2 - 4 with a hole in the graph at the point (0,-4). For the range, I see it as the set of all Reals y where y > -4.