The image provided presents a problem involving the graphing of a rational function. Let's break down the requirements and solve the problem step by step.

Problem Overview:

You're asked to graph the rational function $f(x) = \frac{1}{x^2}$. The tasks include:

1. Finding the inverse.
2. Determining the x-intercept.
3. Identifying the vertical asymptote.
4. Identifying the horizontal asymptote.
5. Filling out the Table of Values.
6. Finally, graphing the function.

Solution Steps:

a. Inverse of the Function

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and solving for $y$.

Given $y = \frac{1}{x^2}$:

1. Swap $x$ and $y$: $x = \frac{1}{y^2}$.
2. Solve for $y$: $y^2 = \frac{1}{x}$ so $y = \pm\frac{1}{\sqrt{x}}$.

Thus, the inverse functions are $y = \frac{1}{\sqrt{x}}$ and $y = -\frac{1}{\sqrt{x}}$, but only for $x > 0$.

b. X-Intercept

To find the x-intercept, set $y = 0$ and solve for $x$:

$0 = \frac{1}{x^2}$

However, $\frac{1}{x^2}$ can never equal 0, so there is no x-intercept.

c. Vertical Asymptote

A vertical asymptote occurs where the function is undefined, which happens when the denominator is zero. For $f(x) = \frac{1}{x^2}$, this occurs at $x = 0$. So, the vertical asymptote is:

$x = 0$

d. Horizontal Asymptote

As $x$ approaches infinity or negative infinity, $\frac{1}{x^2}$ approaches 0. Therefore, the horizontal asymptote is:

$y = 0$

e. Table of Values

Let's calculate the values for the given x-values: