Let me analyze the image and solve the problem based on the graph. One moment, please!### Analyzing the graph and solving the problem:

(a) Determining the domain:

• Graph (a): The function starts at $x = -2$ and extends to $x = 6$ (inclusive).
  The domain is:
  $[-2, 6]$

• Graph (b): The function starts at $x = -4$ and extends to $x = 4$ (inclusive).
  The domain is:
  $[-4, 4]$

(b) Determining the range:

• Graph (a): The graph spans from $y = -6$ (lowest point) to $y = 6$ (highest point), inclusive.
  The range is:
  $[-6, 6]$

• Graph (b): The graph spans from $y = 0$ (lowest point) to $y = 6$ (highest point), inclusive.
  The range is:
  $[0, 6]$

(c) Intervals of increasing, decreasing, and constant behavior:

• Graph (a):

  • Increasing: From $x = -2$ to $x = 2$.
    Interval: $(-2, 2)$
  • Decreasing: From $x = 2$ to $x = 6$.
    Interval: $(2, 6)$

• Graph (b):

  • Increasing: From $x = -4$ to $x = 0$.
    Interval: $(-4, 0)$
  • Decreasing: From $x = 0$ to $x = 4$.
    Interval: $(0, 4)$

Let me know if you’d like me to expand further on these solutions!

5 Related Questions:

1. What is the difference between domain and range in a function?
2. How can you determine the behavior (increasing, decreasing, constant) from a graph?
3. Can the domain or range include infinity, and how is it represented in interval notation?
4. What types of functions correspond to graphs like (a) and (b)?
5. How do turning points affect intervals of increasing and decreasing behavior?

Tip:

When working with interval notation, use brackets $[ ]$ for inclusive values and parentheses $( )$ for exclusive values. Always double-check the endpoints of the graph!