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Sagot :
[tex]f(x)=-4(x+1)^2-3[/tex]
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:
[tex](-\infty,\infty)[/tex]________________________
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.
[tex]f(x)=a(x+h)^2+k[/tex]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:
[tex](-\infty,-3\rbrack[/tex]
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