tonan6e

2022-09-30

How do you graph $f\left(x\right)=\frac{{x}^{2}-1}{x}$ using holes, vertical and horizontal asymptotes, x and y intercepts?

Maddox Koch

Beginner2022-10-01Added 7 answers

You know this graph can't exist at x=0, since that would make the denominator equal 0. Because the polynomial on the top is of a bigger degree, there is a slant asymptote. Dividing the initial terms, we get $\frac{{x}^{2}}{x}=x$, so there is a slant asymptote at y=x.

Since we can factor the top into (x−1)(x+1), we know the function has two solutions at $x=\pm 1$.

Plotting these solutions and following the asymptotes makes this a straightforward graph to sketch: graph{(x^2-1)/x [-10, 10, -5, 5]}

Also, not all rational functions are so easy to pblackict the behavior of, so creating a table of x and y values is always a good idea! And if you need more information about how to find the asymptotes, look here.

Since we can factor the top into (x−1)(x+1), we know the function has two solutions at $x=\pm 1$.

Plotting these solutions and following the asymptotes makes this a straightforward graph to sketch: graph{(x^2-1)/x [-10, 10, -5, 5]}

Also, not all rational functions are so easy to pblackict the behavior of, so creating a table of x and y values is always a good idea! And if you need more information about how to find the asymptotes, look here.

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$