Question

find the open interval(s) where the following function is increasing, decreasing, or constant. express your answer in interval notation.

Explanation:

Step1: Analyze the graph's behavior

For a function \( y = f(x) \), if as \( x \) increases, \( y \) also increases, the function is increasing. If as \( x \) increases, \( y \) decreases, the function is decreasing. A constant function has \( y \) - values that do not change with \( x \).
Looking at the graph (assuming it's a parabola - like part in the positive \( x \) region). Let's assume the vertex of the "U - shaped" part (since it's a function, we consider the right - hand side of the graph which passes the vertical line test) is at \( x = 1\).

Step2: Determine intervals

For \( x>1 \), as \( x \) increases, \( y \) increases.

Answer:

The function is increasing on the interval \( (1,\infty) \)