Recent questions in Rational functions

Rational functions

Given the domain of the rational functions. Write your answers in set notation and interval notation.

Rational functions

For the following exercises, find the domain of the rational functions. $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}-{1}}}{{{x}+{2}}}$$

Rational functions

Fill in the blanks. When evaluating limits at infinity for complicated rational functions, divide the numerator and denominator by the ________ term in the denominator.

Rational functions

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

Rational functions

Determine the domains of the given rational functions. $$\displaystyle\frac{{4}}{{{\left({x}^{{3}}\right)}+{\left({x}^{{2}}\right)}}}$$

Rational functions

Graph the rational functions. $$y=x/((x^2)-2)$$

Rational functions

Choose the correct term to complete each sentence. Limits of polynomial and rational functions can be found by _____, so long as the denominator of the rational function evaluated at c is not 0.

Rational functions

One method of graphing rational functions that are reciprocals of polynomial functions is to sketch the polynomial function and then plot the reciprocals of the y-coordinates of key ordered pairs. Use this technique to sketch $$\displaystyle{y}={\frac{{{1}}}{{{f{{\left({x}\right)}}}}}}$$ for each function. $$a)f(x)=2x,$$ b)f(x)=$$\displaystyle{4}{x}^{{{2}}},$$, $${c}{)}{f{{\left({x}\right)}}}={x}^{{{2}}}-{1}$$ d) $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}$$

Rational functions

Give the range of the rational functions given that neither of the graphs crosses its horizontal asymptote. Write your answers in set notation and interval notation.

Rational functions

Graph the rational functions. Include the graphs and equations of the asymptotes and dominant terms. $$\displaystyle{y}={\frac{{{1}}}{{{2}{x}+{4}}}}$$

Rational functions

Graph the rational functions. $$\displaystyle{y}={\frac{{{x}^{{{2}}}}}{{{x}+{1}}}}$$

Rational functions

Choose the correct term to complete each sentence. Limits of polynomial and rational functions can be found by _____, so long as the denominator of the rational function evaluated at c is not 0.

Rational functions

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?

Rational functions

Involve rational functions that model the given situations. In each case, find the horizontal asymptote as $$\displaystyle{x}→∞$$ and then describe what this means in practical terms. $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{150}{x}+{120}}}{{{0.05}{x}+{1}}}$$ the number of bass. f(x), months in a lake that was stocked with 120 bass.

Rational functions

True or False. Some rational functions have holes in their graph.

Rational functions

Given the domain of the rational functions. Write your answers in set notation and interval notation.

Rational functions

Investigate asymptotes of rational functions. Copy and complete the table. Determine the horizontal asymptote of each function algebraically. Function Horizontal Asymptote $$\displaystyle{f{{\left({x}\right)}}}=\frac{{{x}^{{2}}-{5}{x}{4}}}{{{x}^{{3}}+{2}}}$$ $$\displaystyle{h}{\left({x}\right)}=\frac{{{x}^{{3}}-{3}{x}^{{2}}+{4}{x}-{12}}}{{{x}^{{4}}-{4}}}$$ $$\displaystyle{g{{\left({x}\right)}}}=\frac{{{x}^{{4}}-{1}}}{{{x}^{{5}}+{3}}}$$

Rational functions

Write two different rational functions whose graphs have the same end behavior as the graph of $$y=3x^2$$

Rational functions