Answer:
To graph a cube root function, you can follow these steps:
Determine the domain and range of the function. The domain of the cube root function is all real numbers, and the range is also all real numbers.
Find the intercepts of the function. To find the x-intercept, set the function equal to zero and solve for x. To find the y-intercept, plug in x = 0 and solve for y.
Find the points where the function is undefined, which are the values that make the radicand (the expression under the cube root symbol) negative.
Plot several additional points on the graph by choosing values for x and finding the corresponding values of y by evaluating the function.
Draw the graph by connecting the points with a smooth curve that approaches the x-axis but never touches or crosses it.
Note that the cube root function has a vertical asymptote at x = 0, meaning that the graph approaches the x-axis but never touches or crosses it as x approaches zero from the left or right.