The functions are described below:
- (x + 5) · (x + 1) · (x - 1) · (x - 2)
- (x + 1) · x · (x - 5)
- (x + 5) · (x + 1) · (x - 2)
- (x + 2) · x · (x - 1) · (x - 5)
How to derive the polynomic equations associated to the given graphs
By algebra we know that polynomials can be defined as product of binomials of the following form:
[tex]p(x) = \prod \limits_{i=1}^{n} (x-r_{i})[/tex] (1)
Where:
- x - Independent variable
- [tex]r_{i}[/tex] - Root of the polynomial.
Graphically speaking, a root is an x-value such that p(x) = 0. After observing carefully each graph, we present the following conclusions:
- The first graph have four roots: x₁ = - 5, x₂ = - 1, x₃ = 1, x₄ = 2.
- The second graph have three roots: x₁ = - 1, x₂ = 0, x₃ = 5.
- The third graph have three roots: x₁ = -5, x₂ = - 1, x₃ = 2.
- The fourth graph have four roots: x₁ = -2, x₂ = 0, x₃ = 1, x₄ = 5.
Based on all the information extracted from the four graphs, the polynomic functions are described below:
- (x + 5) · (x + 1) · (x - 1) · (x - 2)
- (x + 1) · x · (x - 5)
- (x + 5) · (x + 1) · (x - 2)
- (x + 2) · x · (x - 1) · (x - 5)
To learn more on polynomials, we kindly invite to check this verified question: https://brainly.com/question/20121808
