Explanation:
a) To determine the end behaviour, we need to sketch the points look on a graph:
[tex]\begin{gathered} As\text{ x }\rightarrow\text{ +}\infty,\text{ f(x)}\rightarrow\text{ -}\infty\text{ (The graph shows oddpower)} \\ As\text{ x }\rightarrow\text{ - }\infty,\text{ f(x) }\rightarrow\text{ +}\infty\text{ } \end{gathered}[/tex]
b) To determine the degree of the polynomial:
We find the difference in f(x) till we get a constant
difference 1: -23-(-4), -4-(3), 3-4, 4 - 5, 5 - 12, 12 - 31
= -19, -7, -1, -1, -7, -19
difference 2: -19-(-7), -7-(-1), -1(-1), -1-(-7), -7-(-19)
= -12, -6, 0, 6, 12
difference 3: -12-(-6), -6-0, 0-6, 6-12
= -6, -6, -6, -6
The constant is seen at the third difference. This is a cubic function
This means degree of the polynomial is 3.
Polynomial is cubic
c) Function in the form f(x) = ax^n
[tex]\begin{gathered} we\text{ n}eed\text{ to find a. We do this by replacing f(x) and x with values:} \\ u\sin g\text{ (x, f(x)) =(}-1,\text{ 3)} \\ f(x)=ax^n \\ \text{where n = degr}ee\text{ = 3} \\ f(x)=ax^3 \\ 3=a(-1)^3 \\ 3\text{ = a(-1)} \\ 3\text{ = -a} \\ a\text{ = -3} \end{gathered}[/tex]
