# Limits of polynomial functinos

• thomasrules
In summary, the task is to invent a function and sketch its graph that satisfies the given conditions: lim_x-0+ f(x)=3 and lim_x-0- f(x)=-2. There are an infinite number of possible functions that could satisfy these conditions, but a simple example would be a piecewise constant function with a constant value for x<0 and a different constant value for x>0.
thomasrules
Invent a function and sketch its graph to satisfy each situation

lim_x-0+ f(x)=3 and lim_x-0- f(x)=-2

I can't figure out an equation for that

Do you mean
$$\lim_{x\rightarrow 0^+} f(x)= 3$$
and
$$\lim_{x\rightarrow 0^-} f(x)= -2$$
?

There are an infinite number of such functions- that's why they say "invent a function". The simplest example is "piecewise constant", a constant for x> 0, another for x< 0.

yes that is what i mean but somethign like $$f(x)=x+3$$ wouldn't work

I said "piecewise constant"- one constant value for x< 0, another for x> 0. What do you think those values should be?

## What is a polynomial function?

A polynomial function is a mathematical function that can be expressed as a sum of terms, each consisting of a constant coefficient multiplied by a variable raised to a non-negative integer power. For example, f(x) = 2x^3 + 5x^2 - 3x + 7 is a polynomial function.

## What are the limits of polynomial functions?

The limits of polynomial functions depend on the degree of the polynomial. A polynomial of degree n will have n+1 possible limits, which can be either positive or negative infinity.

## How do you calculate the limit of a polynomial function?

To calculate the limit of a polynomial function, you can use the standard limit rules to simplify the function until you can directly evaluate the limit. Alternatively, you can use the limit definition of a derivative to find the limit at a specific point.

## What is the significance of the limits of polynomial functions?

The limits of polynomial functions help us understand the behavior of the function as the input value approaches certain values. They can also help us identify the horizontal asymptotes of the function and determine its end behavior.

## Can polynomial functions have any type of limit?

No, polynomial functions can only have horizontal asymptotes as limits. They cannot have vertical asymptotes, since polynomials are continuous functions and do not have any breaks or jumps in their graph.

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