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How do you find the vertex for the function #f(x)=1/x#?

Answer 1

This hyperbola can be written #xy=1#, which is symmetric in #x# and #y#, so the vertices must lie on the line #y = x#, that is at #(1, 1)# and #(-1, -1)#

At the points #(-1, -1)# and #(1, 1)#, where both equations are satisfied, the line #y = x# intersects #y = 1/x#.

graph{[-10, 10, -5, 5]} = 0 (y-x)(xy-1)

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Answer 2

Avery Alexander

To find the vertex of the function ( f(x) = \frac{1}{x} ), you need to first rewrite the function in the standard form of a quadratic function, which is ( f(x) = ax^2 + bx + c ). Then, you can use the formula for finding the vertex of a quadratic function, which is ( (-\frac{b}{2a}, f(-\frac{b}{2a})) ). However, since ( f(x) = \frac{1}{x} ) is not a quadratic function, it doesn't have a vertex in the traditional sense. Instead, it has a vertical asymptote at ( x = 0 ). So, there is no vertex for the function ( f(x) = \frac{1}{x} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.