Ciolan3u
2022-09-11
Answered

What are the asymptotes of $y=\frac{1}{x+3}$ and how do you graph the function?

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asked 2021-02-25

True or False. The graph of a rational function may intersect a horizontal asymptote.

asked 2022-02-16

Does it follow that $r\left(x\right)+p\left(x\right)$ is a rational function (and not a polynomial)?

Suppose$r\left(x\right)\ne 0$ is a rational function (and not a polynomial)

$p\left(x\right)$ is a polynomial function of $x\in \mathbb{R}$ .

Suppose

asked 2022-07-09

Suppose $f\in {O}_{p}(V)$ is a rational function on V that has a value at $p$. Then write $f=a/b={a}^{\prime}/{b}^{\prime}$ where $a,b,{a}^{\prime},{b}^{\prime}\in \mathrm{\Gamma}(V)$, the coordinate ring of V. Want to show the value of $f$ at $p$ is well-defined, i.e. $a(p)/b(p)={a}^{\prime}(p)/{b}^{\prime}(p)$.

So since $a/b={a}^{\prime}/{b}^{\prime}$ are the same equivalence class, there is some non-zero poly $x\in \mathrm{\Gamma}(V)$ such that $x(a{b}^{\prime}-{a}^{\prime}b)=0$. Then $x(p)(a(p){b}^{\prime}(p)-{a}^{\prime}(p)b(p))=0$. Then what? How do we know $x(p)\ne 0$?

So since $a/b={a}^{\prime}/{b}^{\prime}$ are the same equivalence class, there is some non-zero poly $x\in \mathrm{\Gamma}(V)$ such that $x(a{b}^{\prime}-{a}^{\prime}b)=0$. Then $x(p)(a(p){b}^{\prime}(p)-{a}^{\prime}(p)b(p))=0$. Then what? How do we know $x(p)\ne 0$?

asked 2021-06-28

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

b)f(x)=

d)

asked 2022-06-12

I know trigonometric functions such as $7x-6\mathrm{cos}(3x)$ can have an infinite number of critical points, but what about non-zero rational functions? Does it have something to do with how a non-zero polynomial can have a finite number of roots?

asked 2022-05-13

In the case of rational function, when taking the first derivative we take the numerator and find for which point the function is equal to zero.

Now, for the second derivative, can we take the second derivative just of the numerator? it is not intuitive, as we need to take the second derivative of the whole function, but I did not find a counterexample

For example the function: $x+8+\frac{50}{2x-4}$

Now, for the second derivative, can we take the second derivative just of the numerator? it is not intuitive, as we need to take the second derivative of the whole function, but I did not find a counterexample

For example the function: $x+8+\frac{50}{2x-4}$

asked 2021-06-18

Investigate asymptotes of rational functions. Copy and complete the table. Determine the horizontal asymptote of each function algebraically. Function Horizontal Asymptote