# What are the rules for a function to be a polynomial?

## What are the rules for a function to be a polynomial?

In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.

**How do you match a function on a graph?**

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

**Do polynomial functions have restrictions?**

The limit of a polynomial function can be found by finding the sum of the limits of the individual terms. The limit of a function that has been raised to a power equals the same power of the limit of the function. Another method is direct substitution.

### What ideas can you share to easily graph a polynomial function?

Graphing Polynomial Functions

- Find the intercepts.
- Check for symmetry.
- Use the multiplicities of the zeros to determine the behavior of the polynomial at the x-intercepts.
- Determine the end behavior by examining the leading term.
- Use the end behavior and the behavior at the intercepts to sketch the graph.

**What is a function on a graph examples?**

Graphs of functions are graphs of equations that have been solved for y! The graph of f(x) in this example is the graph of y = x2 – 3. It is easy to generate points on the graph. Choose a value for the first coordinate, then evaluate f at that number to find the second coordinate.

**What is the limit of a polynomial?**

The limit of a polynomial function can be found by finding the sum of the limits of the individual terms. The limit of a function that has been raised to a power equals the same power of the limit of the function.

#### What is the range of any polynomial function?

The range of a function is the set of all y-values that the function attains or takes on. The degree of the polynomial is the highest power of x that appears. The numbers a0,a1,…,an are called the coefficients of the polynomial.