Can absolute value functions be considered polynomial functions?

In summary, absolute value functions cannot be considered polynomial functions due to their non-polynomial expression and piecewise definition. They do not have a degree, as it is determined by the highest power of the variable in the function, and must be a non-negative integer for polynomial functions. However, there are some similarities between absolute value and polynomial functions, such as being continuous and having a smooth, unbroken graph with positive and negative values. To graph an absolute value function, you can plot points using the function's definition and apply transformations for more complex functions.
  • #1
LordCalculus
12
0
Are lx3l or lxl3 polynomials?

If not, what would be a good example of a cubic polynomial function (R [tex]\rightarrow[/tex] R) that doesn't cover all real numbers in its codomain?
 
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  • #2
Answer to your first question- no, they are not polynomials.

Answer to your second question, there is none. Every cubic polynomial has range all real numbers.
 

1. Can absolute value functions be considered polynomial functions?

No, absolute value functions cannot be considered polynomial functions because they do not follow the form of a polynomial. Polynomial functions have terms with non-negative integer exponents, while absolute value functions have a piecewise definition with a non-polynomial expression.

2. What is the degree of an absolute value function?

An absolute value function does not have a degree because it is not a polynomial function. The degree of a polynomial function is determined by the highest power of the variable in the function.

3. Can an absolute value function have a negative degree?

No, an absolute value function cannot have a negative degree because it is not a polynomial function. The degree of a polynomial function must be a non-negative integer.

4. Are there any similarities between absolute value functions and polynomial functions?

Yes, there are some similarities between absolute value functions and polynomial functions. Both types of functions are continuous and have a graph that is smooth and unbroken. Additionally, they can both have positive and negative values.

5. How do you graph an absolute value function?

To graph an absolute value function, you can use the function's definition to plot points on a coordinate plane. Remember that the absolute value function has a "V" shape and the graph will reflect across the x-axis for negative values of the input. You can also use transformations, such as shifting and stretching, to graph more complex absolute value functions.

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