list the intercept and test for symmetry y=-8x/x^2+36

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that the the graph of a function intercepts x axis at y = 0, hence, you need to solve the equation `-8x/x^2+36 = 0`  such that:

`-8x/x^2+36 =0 => -8x + 36x^2 = 0`

Factoring out `4x`  yields:

`4x(-2 + 9x) = 0 => 4x = 0 => x = 0`

`-2 + 9x = 0 => 9x = 2 => x = 2/9`

You need to test the symmetry of the graph with respect to x axis, hence, the graph is symmetric with respect to x axis if `f(x) = -f(x)`  such that:

`y = -8x/x^2 + 36 != 8x/x^2 - 36`

Hence, the graph is not symmetric with respect to x axis.

The graph is symmetric with respect to y axis if `f(x) = f(-x)`  such that:

`-8*(-x)/(x^2) + 36 != -8x/x^2 + 36`

Hence, the graph is not symmetric with respect to y axis.

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