Let's break down the mathematical tasks from the image:

1. Function $f(x) = \sqrt{x^2 - 10} + 1$

• (a) Determine the domain and range.
• (b) Explain any restrictions on the domain and range.
• (c) Draw the graph of the function.

2. Given two functions $f(x) = x + 2$ and $g(x) = \frac{1}{x - 3}$, perform:

• (a) Find $(f + g)(x)$ and simplify.
• (b) Find $(f \circ g)(x)$ and simplify.
• (c) Find $(g \circ f)(x)$ and simplify.
• (d) Determine the domain and range of the resulting functions from parts (a), (b), and (c).

3. Consider the line passing through points $A(3, -1)$ and $B(-2, 4)$:

• (a) Calculate the slope.
• (b) Write the equation in point-slope form.
• (c) Convert from point-slope form to slope-intercept form.
• (d) Verify the intercepts by graphing the line.

4. Graph the piecewise function $f(x)$: