the graph shows a vertical translation of y = ∛x. what is the range of the translated function? {y|y < 0}…

the graph shows a vertical translation of y = ∛x. what is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}

the graph shows a vertical translation of y = ∛x. what is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}

Answer

Explanation:

Step1: Recall cube - root function properties

The parent function $y = \sqrt[3]{x}$ has a range of all real numbers, i.e., $(-\infty,\infty)$ or ${y|y\text{ is a real number}}$. A vertical translation of a function $y = f(x)$ to $y=f(x)+k$ (where $k$ is a constant) does not change the range of the function.

Step2: Determine the range of the translated function

Since the range of $y = \sqrt[3]{x}$ is all real numbers and vertical translation does not affect the range, the range of the translated function is also all real numbers.

Answer:

{y|y is a real number}