c. Choose two functions from any set. Find the slope between consecutive points on the graphs.

CMIIh
2021-09-15
Answered

Consider the following sets of rational functions. $af\left(x\right)=\frac{a}{x}$ for a={−2,−1,−0.5,0.5,2,4}, $h(x-c)=\frac{1}{x-c}$ for c=[−4,−2,−0.5,0.5,2,4], h(x−c)=1x−c for c=[−4,−2,−0.5,0.5,2,4], g(bx)=1bx for b={−2,−1,−0.5,0.5,2,4} for b={−2,−1,−0.5,0.5,2,4}, $k\left(x\right)+d=\frac{1}{x}+d$ for d={−4,−2,−0.5,0.5,2,4} for d={−4,−2,−0.5,0.5,2,4}.

c. Choose two functions from any set. Find the slope between consecutive points on the graphs.

c. Choose two functions from any set. Find the slope between consecutive points on the graphs.

You can still ask an expert for help

Laith Petty

Answered 2021-09-16
Author has **103** answers

For the first set slopes are 0.5 and 1, for the second set slopes are -0.5 and 0.5 for the third set slopes are

asked 2021-02-25

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

asked 2022-02-15

In general, how does one determine if a rational function is regular? I have the particular problem of determining in which points of the circle $V({x}^{2}+{y}^{2}-1)\subseteq {A}^{2}$ is the rational function $\alpha =\frac{y-1}{x}$ regular?

asked 2022-02-15

"A rational function is defined as the quotient of polynomials in which the denominator has a degree of at least 1"

If we are talking merely about x, then I get the concept. A rational function f(x) could be written as "

The issue that I'm having is that of talking about rational functions of n variables. For instance, what would be the meaning of 'f(x,y) is a rational function of

asked 2022-05-17

Suppose you have a rational function, of the form $H(x)=\frac{B(x)}{A(x)}$. It's differential is of the form ${H}^{\prime}(x)=\frac{({B}^{\prime}(x)\star A(x)-B(x)\star {A}^{\prime}(x))}{(A(x){)}^{2}}$. It is trivial to prove that, if $k$ is a root of $B(x)$ or $A(x)$ with rank $r$, $r\ge 2$, then k is also a root of ${H}^{\prime}(x)$'s numerator, ${B}^{\prime}(x)\star A(x)-B(x)\star {A}^{\prime}(x)$, with rank at least $r-1$. Is there a theorem that states this exact thing?

The reason I need this is, I am going to take an exam soon, and in a specific part of the exam this observation would be very useful. But I will have to prove it by hand during the exam, and time will be very limited, so I was wondering if there is already a name for this to reference it directly and get on with it.

EDIT: Had erroneously named the desired form "polynomial fraction", instead of the right "rational function".

The reason I need this is, I am going to take an exam soon, and in a specific part of the exam this observation would be very useful. But I will have to prove it by hand during the exam, and time will be very limited, so I was wondering if there is already a name for this to reference it directly and get on with it.

EDIT: Had erroneously named the desired form "polynomial fraction", instead of the right "rational function".

asked 2021-05-22

Do all rational functions have vertical asymptotes? Why or why not? If not, give an example of a rational function that does not have a vertical asymptote.

asked 2022-05-07

Find all the points of discontinuity of the function $\frac{{y}^{2}-18y+80}{(y-4)(y-1)}$.

asked 2021-09-13

Use substitution to convert the integrals to integrals of rational functions. Then use partial fractions to evaluate the integrals.

$\int \frac{1-\sqrt{x}}{1+\sqrt{x}}dx$