Graph the function $f(x)=-\sqrt[3]{x}$ using the techniques of shifting, compressing, stretching, and or refiecting Start with the graph of the basic function (for example, $y=x^{2}$ ) and show all the steps. Be sure to show at least three key points. Find the dornain and the range of the function.

Choose the correct graph below.
A.
B.
c.
D.

The domain of $\mathrm{f}$ is $\square$
(Type your answer in interval notation)
The range of $\mathrm{t}$ is $\square$
(Type your answer in interval notation)

Step 1 ：Understand the function $f(x)=-\sqrt[3]{x}$. This is a cubic root function, which is reflected over the x-axis due to the negative sign.

Step 2 ：The domain of this function is all real numbers, because you can take the cubic root of any real number. The range is also all real numbers, because the cubic root function can output any real number.

Step 3 ：Identify key points on the graph. For the basic cubic root function $y=\sqrt[3]{x}$, we know that when $x=0$, $y=0$, when $x=1$, $y=1$, and when $x=-1$, $y=-1$. Since our function is reflected over the x-axis, the y-values of these points will be negated.

Step 4 ：Graph the function by plotting the key points and drawing a smooth curve through them.

Step 5 ：The domain of $f$ is $(-\infty, \infty)$ and the range of $f$ is also $(-\infty, \infty)$. The graph of the function $f(x)=-\sqrt[3]{x}$ is a reflection of the graph of $y=\sqrt[3]{x}$ over the x-axis. The key points are $(0,0)$, $(1,-1)$, and $(-1,1)$.

Step 6 ：\(\boxed{\text{The domain of } f \text{ is } (-\infty, \infty) \text{ and the range of } f \text{ is also } (-\infty, \infty)}\)