Question

Please attached.

Answer 1

The answer is really not that important. I really what to know what the expression is telling me.

Answer 2

The graph is like this

Answer 3

the lowest point is -4

Answer 4

Range of f(x) means f(x) is between which two values
from the graph,
-4<f(x)

Answer 5

i understand that, what about the....if x is =0 what does that mean and how does it effect the graph??

Answer 6

and whats with the 5 as well

Answer 7

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

Answer 8

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.