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Question

Find domain and range of the function
f(x)=-3x^2-15x+12

S varies jointly as p and q. If p= 13 and q= 15, then S = 80. Write S as a function of p and q.

S=?

Answer 1

[updated]
Any good math answer involves some calculations, but the answer to the first example is provided here: the range of this function includes all of the solutions to the process of the function; and, the domain of the function is a given real number as 'x'. Often, we include the range from a domain like {x | -3 < x < 3} when drawing the graph. The range of a function sounds like this big, expansive set of solutions. Really it's the dependent multi-"part" of a function and corresponds as an y-coordinate.

Answer 2

f(x) = -3x^2 - 15x + 12
It's a polynomial, so the domain is the whole real line.
Since the leading coefficient is negative, we know it has a maximum at x = -b/2a = 15/(-6) = -5/2.
f(-5/2) = -3(25/4) - 15 (-5/2) + 12 = -75/4 + 75/2 + 12 = 123/4. So the range is (-∞, 123/4].

S = kpq for some constant k. So 80 = k(13)(15), i.e. k = 80/195 = 16/39. So S = (16/39) pq.

Answer 3

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