# What are the cut points of a rational function?

Question
Rational functions

What are the cut points of a rational function? Explain how to solve a rational inequality.
$$check_{circle}$$
$$thumb_{up}$$
$$thumb_{down}$$
Step 1
Calculus homework question answer, step 1, image 1
Step 2
Calculus homework question answer, step 2, image 1
Explore similar questions
$$thumb_{up}$$
$$thumb_{down}$$

2021-02-15

Let $$r(x)=P(x)/Q(x)$$ is a rational function
The cut point of the function r(x) are the values of the x at which either
$$P(x)=0$$ or $$Q(x)=0$$
To find the rational inequality use the test points between the successive cut points to find the interval that satisfies the inequality

### Relevant Questions

For what value of the constant c is the function f continuous on $$\displaystyle{\left(−∞,+∞\right)}?$$
 $$\displaystyle{f{{\left({x}\right)}}}={\left\lbrace{\left({c}{x}^{{2}}\right)}+{4}{x},{\left({x}^{{3}}\right)}-{c}{x}\right\rbrace}{\quad\text{if}\quad}{x}{<}{5},{\quad\text{if}\quad}{x}\Rightarrow{5}$$ c=

The graph is a translation of the graph of f(x) = 2x². Write the function for the graph in vertex form.

left $$f(x)=2^{\sin(x)}$$
Find f'(x)

What is the slope of a line perpendicular to the line whose equation is $$x - y = 5$$. Fully reduce your answer.

Use the piecewise-defined function to fill in the bla
.
$$\displaystyle{f{{\left({x}\right)}}}={\left\lbrace{4},-{4}{<}{x}{<}-{2},{2}{x}-{4},-{1}{<}{x}{<}{2},{3}{x},{2}\le{x}{<}{5}\right\rbrace}$$
a. The domain ____ is used when graphing the function $$f(x)=2x-4$$.
b. The equation ____ is used to find $$f(4)=12.$$

A surface is represented by the following multivariable function,
$$\displaystyle{f{{\left({x},{y}\right)}}}=\frac{{1}}{{3}}{x}^{{3}}+{y}^{{2}}-{2}{x}{y}-{6}{x}-{3}{y}+{4}$$
a) Calculate $$\displaystyle{f}_{{x x}},{f}_{{{y}{x}}},{f}_{{{x}{y}}}{\quad\text{and}\quad}{f}_{{{y}{y}}}$$
b) Calculate coordinates of stationary points.
c) Classify all stationary points.

Evaluate the piecewise defined function at the indicated values.
$$a^m inH$$
$$f(x)= \begin{array}{11}{5}&\text{if}\ x \leq2 \ 2x-3& \text{if}\ x>2\end{array}$$
$$a^m inH$$
f(-3),f(0),f(2),f(3),f(5)

$$\sec \theta = -3, \tan \theta > 0$$. Find the exact value of the remaining trigonometric functions of
$$\theta$$.

Use long division to rewrite the equation for g in the form
$$\text{quotient}+\frac{remainder}{divisor}$$
Then use this form of the function's equation and transformations of
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}}}}$$
to graph g.
$$\displaystyle{g{{\left({x}\right)}}}={\frac{{{2}{x}+{7}}}{{{x}+{3}}}}$$

$$\begin{array}{|c|c|}\hline x & y \\ \hline 1 & 2 \\ \hline 2 & 4 \\ \hline 3 & 8 \\ \hline 4 & 16 \\ \hline 5 & 32 \\ \hline \end{array}$$
Write a linear $$(y=mx+b),$$ quadratic $$(y=ax2)$$, or exponential $$(y=a(b)x)$$ function that models the data.
$$y=?$$