Let's go through the parts of the problem one by one based on the graph described.

(a) Domain of $f$

The domain of a function is the set of all possible $x$-values for which the function is defined. The graph shows that the function has values starting from $x = -\infty$ to $x = \infty$, as it includes a ray extending indefinitely to the left. Hence, the domain is:

$(-\infty, \infty)$

(b) Range of $f$

The range of a function is the set of all possible $y$-values. From the graph, the lowest $y$-value occurs at $y = -1$ (at $x = 5$). The function increases upwards indefinitely after that. So, the range is:

$[-1, \infty)$

(c) $x$-intercepts of $f$

The $x$-intercepts are the points where the function crosses the $x$-axis. Based on the graph, the curve crosses the $x$-axis at $x = 4$ and $x = 6$. Therefore, the $x$-intercepts are:

$x = 4 \quad \text{and} \quad x = 6$

(d) $y$-intercept of $f$

The $y$-intercept is the point where the function crosses the $y$-axis. The graph shows that the function crosses the $y$-axis at $(0, 24)$. Therefore, the $y$-intercept is:

$y = 24$

(e) Intervals on which $f$ is increasing

A function is increasing on intervals where its slope is positive. Based on the graph:

• The curve rises from $x = 5$ to $x = 7$.
• The ray extending to the left is horizontal, so it doesn't count as increasing.

Thus, $f$ is increasing on the interval:

$(5, 7)$

Would you like more details or have any questions? Here are five related questions that extend the concepts:

1. What are the intervals where $f$ is decreasing?
2. How do we find intervals where $f$ is constant from a graph?
3. What is the significance of the relative minimum?
4. Can a function have multiple $y$-intercepts? Why or why not?
5. How does the behavior of the function indicate whether it is even, odd, or neither?

Tip: Always pay attention to the slope of a function to determine increasing or decreasing intervals.