Let's examine the function given:

$g(r) = (r - 2)(r + 4)(r - 1)$

To find the g-intercept and r-intercepts:

1. g-intercept: The g-intercept occurs when $r = 0$. Substitute $r = 0$ into $g(r)$:

   $g(0) = (0 - 2)(0 + 4)(0 - 1) = (-2)(4)(-1) = 8$

   So, the g-intercept is $8$.

2. r-intercepts: The r-intercepts occur when $g(r) = 0$. Set each factor of $g(r)$ equal to zero:

   $(r - 2) = 0 \Rightarrow r = 2$ $(r + 4) = 0 \Rightarrow r = -4$ $(r - 1) = 0 \Rightarrow r = 1$

   Therefore, the r-intercepts are $r = 2$, $r = -4$, and $r = 1$.

Final Answers:

• g-intercept: $8$
• r-intercepts: $2, -4, 1$

Would you like further details or explanations on how these intercepts were calculated?

Here are 5 related questions for further exploration:

1. What is the degree of the polynomial function $g(r)$?
2. How would you find the end behavior of the function $g(r)$?
3. Can you determine the sign of $g(r)$ at values just above and below each intercept?
4. What is the expanded form of $g(r)$?
5. How would the graph of $g(r)$ look based on its intercepts and end behavior?

Tip: For any polynomial, finding intercepts by setting $x = 0$ (for y-intercept) and solving $y = 0$ (for x-intercepts) provides quick insights into its behavior.