Math Problem Statement
Given the function g(n)=(n-2)(n+5)(n-3):
the coordinates of its g-intercept are
the coordinates of its n-intercepts are
Solution
Let's analyze the given function to find its intercepts.
1. g-intercept (y-intercept):
The g-intercept occurs when . So, substitute into the function:
Thus, the coordinates of the g-intercept are:
2. n-intercepts (x-intercepts):
The n-intercepts occur where . Set the function equal to 0:
This equation is satisfied when any of the factors equals zero:
Thus, the coordinates of the n-intercepts are:
Summary:
- g-intercept:
- n-intercepts:
Do you have any questions or want further details?
Here are some related questions to consider:
- How do you find the vertex of a quadratic or cubic function?
- What does the sign of the leading coefficient tell you about the graph of the function?
- How can you use the factored form of a polynomial to sketch its graph?
- What is the significance of multiple roots in a polynomial function?
- How does the degree of a polynomial function affect its general shape?
Tip: When finding intercepts, always plug for the g-intercept and set the function equal to zero for the n-intercepts.
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Math Problem Analysis
Mathematical Concepts
Polynomial Functions
Factoring
Intercepts
Formulas
g(n) = (n - 2)(n + 5)(n - 3)
n-intercept: g(n) = 0
g-intercept: g(0)
Theorems
Zero Product Property
Factored Form of Polynomials
Suitable Grade Level
Grades 9-11
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