https://file.aiquickdraw.com/mathbot/file/17303183131489cjbsqwq.jpg

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?

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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.

Given the function g(r) = (r - 2)(r + 4)(r - 1), its g-intercept is ______, and its r-intercepts are ______.

Learn how to find the g-intercept and r-intercepts of the polynomial function g(r) = (r - 2)(r + 4)(r - 1). This problem covers key algebraic concepts such as polynomial functions and the Zero Product Property. Suitable for high school students in Grades 9-11.

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