Question

Determine an algebraic model of a function that satisfies the following key features.

Answer 1

Given the conditions;

`As\text{ }x\rightarrow-\infty,y\rightarrow\infty\text{ and }x\rightarrow\infty,y\rightarrow\infty`

When;

`x\rightarrow-\infty,y\rightarrow\infty`

Then, the degree of the polynomial is even.

Then, given three x-intercepts, it means one of the root could have been repeated.

Thus, the model function is;

`f\lparen x)=\left(x+1\right)\left(x-3\right)\left(x^2\right)`