You can put this solution on YOUR website! Determine the domain and range of the function y=-x^2 + 6x - 8.
Domain has to do with what your x values are allowed to be. The domain of all polynomial functions is: all real numbers. There are no restrictions on what x can be.
Set builder notation for the domain would be: {x|x is all real numbers}
Interval notation would be: x=(-infinity,infinity) I can't do the infinity symbols yet.
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Range has to do with what the y values are given that the function's domain is what it is.
For quadratic functions, the range is found through the vertex and whether the graph is opening up or down.
The coefficient of x^2 is negative, therefore our parabola opens downward and goes to negative infinity. It's vertex is at its maximum height. We can find the vertex with the formula: , our a=-1, b=6 and c=-8
The maximum y value will happen when x=3:
Therefore the range is: - infinity to 1
(-infinity,1] <---- interval notation
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If you don't have to do this algebraically and you can use a graphing calculator, then graph the equation:
The x's extend forever left and right, the y' go from 1 down to -infinity.
Happy Calculating!!!
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