Answer:
The range of the function is: -∞≤y≤∞.
Step-by-step explanation:
Consider the provided function
[tex]y=\sqrt[3]{x+8}[/tex]
The range of the function is the set of all values which a function can produce or the set of y values which a function can produce after substitute the possible values of x.
The range of a cubic root function is all real numbers.
Now consider the provided function.
[tex]y=\sqrt[3]{x+8}[/tex]
The above function can be written as:
[tex]y=(x+8)^{\frac{1}{3}}[/tex]
Taking cube on both sides.
[tex]y^3=x+8\\\\x=y^3-8[/tex]
The graph of the function is shown in figure 1:
For any value of x we can find different value of y.
Here, the cube root function can process negative values. Since, the function can produce any values, the range of the given function is -∞≤y≤∞ .
Therefore, the range of the function is: -∞≤y≤∞.
