Example 1 Study the domain, parity, monotonicity, and maximum or minimum value of the function $y=x^{\frac{4}{3}}$, and draw its graph.
(1) The domain of the function $y=f(x)=x^{\frac{1}{3}}=\sqrt[3]{x^{4}}$ is $\mathbf{R}$.
(2) For any $x \in \mathbf{R}$, we have $f(-x)=\sqrt[3]{(-x)^{4}}=\sqrt[3]{x^{4}}=f(x)$, so the function $y=x^{\frac{4}{3}}$ is an even function.
(3) Let $x_{1} 、 x_{2} \in[0,+\infty)$, and $x_{1}<x_{2}$. By the properties of inequalities, we get $x_{1}^{4}<x_{2}^{4}$, thus $\sqrt[3]{x_{1}^{4}}<\sqrt[3]{x_{2}^{4}}$, which means $f\left(x_{1}\right)<f\left(x_{2}\right)$.
Therefore, the function $y=x^{\frac{1}{3}}$ is increasing on the interval $[0,+\infty)$. 
By the symmetry of the graph of an even function about the $y$-axis, we know that the function $y=x^{\frac{4}{3}}$ is decreasing on the interval $(-\infty, 0]$.
(4) From the monotonicity of the function $y=x^{\frac{4}{3}}$, we know that $y_{\text {min }}=$ $f(0)=0$, and there is no maximum value.
(5) By the properties of even functions, first list and plot the points to draw the graph of the function $y=x^{\frac{1}{3}}$ within $[0,+\infty)$, then draw the graph symmetric about the $y$-axis, as shown in Figure 4-2.
Figure 4-2
Solution Guidance: The study of the properties of the function here starts from the definition, involving calculations and arguments, and finally uses the properties of the function to list, plot points, and draw the graph of the function. This is completely different from the method of first listing, plotting points, and drawing the graph of the function, and then describing the properties of the function from the graph.