Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Properties of Square Root Function

Let f(x) = sqrt{ x } be the square root function.

1. Why is the function neither even or odd?

If I let x be -x, I get sqrt{-x}. I don't understand why the square root function is neither even or odd.

2. Why does the function have an absolute minimum of 0 at x = 0?

I say because the graph of f(x) = sqrt{x} begins to rise from the origin where x = 0.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Properties of Square Root Function

To test a function with respect to odd/even you have to be able to try -x in place of x. But the function isn't defined for negatives so you cannot do the test.  Or, to investigate by inspecting the graph: has it got reflective symmetry in the y axis or rotational symmetry around (0,0) ? No because there are no negtaive points on the curve.

Your answer for part 2 is correct.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Properties of Square Root Function

To test a function with respect to odd/even you have to be able to try -x in place of x. But the function isn't defined for negatives so you cannot do the test.  Or, to investigate by inspecting the graph: has it got reflective symmetry in the y axis or rotational symmetry around (0,0) ? No because there are no negtaive points on the curve.

Your answer for part 2 is correct.

Bob

Perfect. Thanks.