Question

determine all intervals on which the graph of f is increasing. graph of f (with coordinate plane and function graph) answer attempt 1 out of 2 additional solution no solution submit answer (symbols like ∞, ≤, ≥, , ), (, ) all real numbers)

Explanation:

Step1: Recall the definition of an increasing function

A function \( f(x) \) is increasing on an interval if, as \( x \) increases (moves from left to right along the x - axis), the value of \( f(x) \) (the y - value) also increases. Geometrically, this means the graph of the function rises from left to right on that interval.

Step2: Analyze the graph of \( f \)

• First, look at the left - most part of the graph. From \( x=-8 \) to \( x = 0 \), the graph is decreasing (since as \( x \) increases from - 8 to 0, the y - values decrease).
• Then, from \( x = 0 \) to \( x=4 \), as we move from left to right (increase \( x \) from 0 to 4), the y - values of the function are increasing (the graph is rising).
• Next, from \( x = 4 \) to \( x = 6 \), as \( x \) increases from 4 to 6, the y - values decrease (the graph is falling).
• Finally, from \( x=6 \) to \( x=\infty \) (or as \( x \) increases beyond 6), the y - values of the function are increasing (the graph is rising again).

Answer:

The function \( f(x) \) is increasing on the intervals \( (0, 4)\) and \( (6, \infty) \)