# 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.