Answer:
The value of [tex]y=\dfrac{10}{x^{2}}[/tex] will always be positive and will be above [tex]x[/tex]-axis.
Step-by-step explanation:
The negative or positive value of 'y' depends on the function itself i.e. the nature of [tex]x[/tex].
For example,
- The negative or positive sign associated with terms of [tex]x[/tex]. For example: [tex]y = -x^3[/tex] will always be negative.
- The functions like modulus or even powers of [tex]x[/tex]. For example [tex]y = |x|[/tex] will always be positive and above [tex]x[/tex] axis i.e. no part below [tex]x[/tex]-axis.
In the current scenario, we are given the function
[tex]y=\dfrac{10}{x^{2}}[/tex]
Here, we have even power of [tex]x[/tex] and the sign associated with [tex]x[/tex] is also positive.
So, value of [tex]y[/tex] will always be positive.
If we provide value of [tex]x[/tex] as negative, even then we will get value of [tex]y[/tex] as positive because the value of [tex]x[/tex] is squared.
Please refer to the graph attached for the function:
[tex]y=\dfrac{10}{x^{2}}[/tex]
