\(f(x)=|x|\) is the simplest parent. This graph has a V shape where the point of the V is at the origin. h(x) has a similar shape but the point of the V is not at the origin but at the point (-3,-5).

Question

asked 2021-05-09

For the following exercises, find the domain of the rational functions.

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{4}{x}-{3}}}{{{x}^{{{4}}}-{5}{x}^{{{2}}}+{4}}}}\)

\(\displaystyle{f{{\left({x}\right)}}}={\frac{{{x}^{{{2}}}+{4}{x}-{3}}}{{{x}^{{{4}}}-{5}{x}^{{{2}}}+{4}}}}\)

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)?

\(\displaystyle{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}\)

\(\displaystyle{t}{\left({x}\right)}=\frac{{{x}^{{3}}-{9}{x}}}{{{x}+{2}}}\)

\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}-{6}}}{{{x}^{{2}}-{25}}}\)

\(\displaystyle{w}{\left({x}\right)}=\frac{{{x}^{{3}}+{6}{x}^{{2}}+{9}{x}}}{{{x}+{3}}}\)

What are the asymptotes of the function r(x)?

asked 2021-06-07

\(\displaystyle{s}{\left({x}\right)}=\frac{{{x}^{{3}}+{27}}}{{{x}^{{2}}+{4}}}\)

\(\displaystyle{t}{\left({x}\right)}=\frac{{{x}^{{3}}-{9}{x}}}{{{x}+{2}}}\)

\(\displaystyle{u}{\left({x}\right)}=\frac{{{\left({x}^{{2}}\right)}+{x}-{6}}}{{{x}^{{2}}-{25}}}\)

\(\displaystyle{w}{\left({x}\right)}=\frac{{{x}^{{3}}+{6}{x}^{{2}}+{9}{x}}}{{{x}+{3}}}\)

What are the asymptotes of the function r(x)?

asked 2021-06-13

Give a example of two functions h(x) and g(x), such that (h o g) (x) does not exist.