Does the graph of the function y=3√^3(x-1)

Question

show that the function is increasing or decreasing?(1 point)
Responses

increasing
increasing

decreasing
decreasing

Neither increasing nor decreasing
Neither increasing nor decreasing

Both increasing and decreasing

Answer 1

To determine whether the function \( y = 3\sqrt[3]{x-1} \) is increasing or decreasing, we can analyze its behavior.

1. Understanding the Function: The term \( \sqrt[3]{x-1} \) means we are taking the cube root of \( x-1 \). The cube root function is defined for all real numbers and is increasing. Therefore, as \( x \) increases, \( \sqrt[3]{x-1} \) also increases.

2. Multiplication by a Positive Constant: The entire function is multiplied by 3, which is a positive constant. Multiplying an increasing function by a positive constant preserves the increasing nature.

3. Conclusion: Since \( \sqrt[3]{x-1} \) is increasing and positive, \( y = 3\sqrt[3]{x-1} \) is also increasing.

Thus, the graph of the function shows that it is increasing.