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Determine the domain and range of the quadratic function. f(x)=−4(x+1)^2−3 Enter your answer in interval notation.

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f(x)=-4(x+1)^2-3

Domain: Set of x-values for which the function is defined.

The given function is a quadratic function, the quadratic functions are defined for all values of x.

The domain of the given quadratic function is:


(-\infty,\infty)

________________________

Range: Set of y-values that takes the function.

To identify the range of a quadratic function you need to find the vertex and identify if the parabola opens up or down.


f(x)=a(x+h)^2+k

The given function is written in the vertex form. The coordinates of the vertex are (h,k).

A parabola opens up if a>0

A parabola opens down if a<0

Given function:

a= -4. The parabola opens down

Vertex: (-1,-3)

As the parabola opens down the y-coordinates of the vertex is the maximum value of the function (parabola goes from y = -∞ to y= -3)

The range of the given quadratic function is:


(-\infty,-3\rbrack

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