Answer
The graph is shown below:
Work Step by Step
Consider the functions $y=\frac{1}{x},y=\frac{1}{{{x}^{3}}},$ and $y=\frac{1}{{{x}^{5}}}$.
Step 1: Write the functions $y=\frac{1}{x}$ , $y=\frac{1}{{{x}^{3}}},$ and $y=\frac{1}{{{x}^{5}}}$.
Step 2: Set the window $\left( -5,5,1 \right)$ and $\left( -5,5,1 \right)$.
Step 3: Plot the graph.
In the graph, the slope of the function $y=\frac{1}{{{x}^{5}}}$ approaches zero faster than the other two functions $y=\frac{1}{{{x}^{3}}},y=\frac{1}{x}$.
The function $y=\frac{1}{{{x}^{3}}}$ approaches zero faster than function $y=\frac{1}{x}$.
In general, the graph of the function $y=\frac{1}{{{x}^{n}}}$ approaches zero faster as the n value increases.
Therefore, as $x$ tends to zero, the graph of the function $y=\frac{1}{x}$ approaches infinity faster than the other two functions.
