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How do you find the range in statistics?
What is the range of a list of numbers?
Which of the following is the formula for range?
Here's a method without calculus.
Let $f(x)=y=\frac{x^2+6}{2x+1}\Rightarrow 2xy+y=x^2+6\Rightarrow x^2-2xy+6-y=0\Rightarrow x=\frac{2y±\sqrt{4y^2-24+4y}}{2}$ Denominator can never be $0$ in this case. So the domain depends only upon $4y^2-24+4y\Rightarrow 4y^2+4y-24≥0\Rightarrow 4(y-2)(y+3)≥0\Rightarrow (y-2)(y+3)≥0\Rightarrow y\in(- \infty, -3]\cup[2,\infty).$
Hence the range of the $f(x)$ is $(- \infty, -3]\cup[2,\infty)$
I guess you know solving inequalities...
To find the range of a function, my first instinct is to check whether the graph has an inverse. We can do this informally using the Horizontal Line Test. If no Horizontal Line intersects the function more than once, then the function has an inverse. With that, we can find $f(y) = x$. The "domain" of $f(y)$ would be the range of the function $f(x)$.
Else, we can use the derivatives of the function to help us find the maximum and minimum which gives us the lower and upper bound of the range of $f(x)$.
Hey so, I jumped a math class and I have a big test coming. I know how to find the domain of a function without a graph, but how do you find the range? The range of a function without a graph, I mean. They discussed it in the class before this one but I wasn't there and the notes aren't telling me much. If there isn't a specific way, are there any tips or tricks? Specifically quadratic functions or functions with square roots in them? My teacher in his notes just replaces the radicand or any other number in a parentheses like thing with [0, infinity)