Question

Consider the statement, “All polynomial functions are rational functions.” Is this statement true? Explain your thinking.

Rational functions
ANSWERED
asked 2021-07-01
Consider the statement, “All polynomial functions are rational functions.” Is this statement true? Explain your thinking.

Answers (1)

2021-07-02
Every polynomial p(x) can be represented as \(\displaystyle{p}\frac{{{x}}}{{1}}\). As y=1 is trivially a polynomial we conclude that the statement is TRUE.
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-05-22
Describe the key characteristics of the graphs of rational functions of the form \(\displaystyle{f{{\left({x}\right)}}}=\frac{{{a}{x}+{b}}}{{{c}{x}+{d}}}\). Explain how you can determine these characteristics using the equations of the functions. In what ways are the graphs of all the functions in this family alike? In what ways are they different? Use examples in your comparison.
asked 2021-05-17
Describe the key characteristics of the graphs of rational functions of the form \(\displaystyle{f{{\left({x}\right)}}}=\frac{{{a}{x}+{b}}}{{{c}{x}+{d}}}\). Explain how you can determine these characteristics using the equations of the functions. In what ways are the graphs of all the functions in this family alike? In what ways are they different? Use examples in your comparison.
asked 2021-05-03
Consider the following rational functions: \(\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}-{1}}}{{{x}^{{2}}-{x}-{2}}}\).
\(\displaystyle{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}\)
\(\displaystyle{t}{\left({x}\right)}=\frac{{{x}^{{3}}-{9}{x}}}{{{x}+{2}}}\)
\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}-{6}}}{{{x}^{{2}}-{25}}}\)
\(\displaystyle{w}{\left({x}\right)}=\frac{{{x}^{{3}}+{6}{x}^{{2}}+{9}{x}}}{{{x}+{3}}}\)
What are the asymptotes of the function r(x)?
asked 2021-06-07
Consider the following rational functions: \(\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}-{1}}}{{{x}^{{2}}-{x}-{2}}}\).
\(\displaystyle{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}\)
\(\displaystyle{t}{\left({x}\right)}=\frac{{{x}^{{3}}-{9}{x}}}{{{x}+{2}}}\)
\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}-{6}}}{{{x}^{{2}}-{25}}}\)
\(\displaystyle{w}{\left({x}\right)}=\frac{{{x}^{{3}}+{6}{x}^{{2}}+{9}{x}}}{{{x}+{3}}}\)
What are the asymptotes of the function r(x)?
asked 2021-05-25
Choose the correct term from the list above to complete each sentence. Power, radical, polynomial. and rational functions are examples of _____.
asked 2021-05-14
Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).
asked 2021-06-23
This ideal gas law states that the volume of an enclosed gas at a fixed temperature varies inversely as the pressure.
Which power functions are also rational functions?
asked 2021-05-01
Consider the following rational functions: \(\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}−{1}}}{{{\left({x}^{{2}}\right)}−{x}−{2}}}\)
\(\displaystyle{s}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}+{27}}}{{{\left({x}^{{2}}\right)}+{4}}}\)
\(\displaystyle{t}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}−{9}{x}}}{{{x}+{2}}}\)
\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}−{6}}}{{{\left({x}^{{2}}\right)}−{25}}}\)
\(\displaystyle{w}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}+{\left({6}{x}^{{2}}\right)}+{9}{x}}}{{{x}+{3}}}\)
Which of these rational functions has a horizontal asymptote?
asked 2021-05-26
Consider the following rational functions: \(\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}−{1}}}{{{x}^{{2}}}}−{x}−{2}{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}\)
\(\displaystyle{t}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}−{9}{x}}}{{{x}+{2}}}\)
\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}−{6}}}{{{x}^{{2}}−{25}}}\)
\(\displaystyle{w}{\left({x}\right)}={\left({\left({x}^{{3}}\right)}+{\left({6}{x}^{{2}}\right)}+{9}{x}\right)}\frac{{)}}{{{x}+{3}}}\)
Which of these functions has no vertical asymptote?
asked 2021-06-05
Consider the following rational functions: \(\displaystyle{r}{\left({x}\right)}=\frac{{{2}{x}−{1}}}{{{\left({x}^{{2}}\right)}−{x}−{2}}}\)
\(\displaystyle{s}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}+{27}}}{{{\left({x}^{{2}}\right)}+{4}}}\)
\(\displaystyle{t}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}−{9}{x}}}{{{x}+{2}}}\)
\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}−{6}}}{{{\left({x}^{{2}}\right)}−{25}}}\)
\(\displaystyle{w}{\left({x}\right)}=\frac{{{\left({x}^{{3}}\right)}+{\left({6}{x}^{{2}}\right)}+{9}{x}}}{{{x}+{3}}}\)
Which of these rational functions has a horizontal asymptote?

You might be interested in

...