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Whats the domain and range explain in words,

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q(x)=-3 (x+2)^2+9?

asked Nov 1, 2014 in PRECALCULUS by anonymous

1 Answer

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The function q(x) = - 3(x + 2)2 + 9

y = - 3[x - (- 2)]2 + 9

The above function represents vertex form of  parbola.

We know that the parabola like curve.

y = - 3[ x - (- 2)]2 + 9

Compare it to vertex form of parabola y = a (x - h)2 + k.

a = - 3, h = - 2, k = 9

(h, k ) = (x, y)

a is negative number the parabola opens down and has maximum value.

When the parabola opens down it has a maximum point which is the vertex of parabola (- 2, 9).

We know that domain of the function is all possible x values and range is all posible y values.

Parabola domain x =  all real numbers.

In the maximum point y = 9  so the graph of parabola cannot be upper than 9.

Thus the range of function y ≤ 9.

Domain of function is all real numbers.

Range of the function is  {y ∈ R : y  ≤ 9}.

answered Nov 1, 2014 by david Expert

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