Question

f(x)=-1/(x+1)^2

find the vertical asymptote
horizontal asymtote
slanted asymtote
x int
y int
holes
domain
and range

Answer 1

please don't make it complicated, its late and i need sleep

Answer 2

never mind! instead do it for the equation 2x^2-x-1/x^2-4x=3

Answer 3

@vishweshshrimali5

Answer 4

Vertical Asymptote:
Factor out denominator... x(x-4)

Answer 5

Vertical asymptote: \((x+1)^2=0\)

Answer 6

on my calculator it says the va is 3?

Answer 7

No.

Answer 8

Yes, 3 is ONE of the V A's

Answer 9

\[(x+1)^2=0\]Solve for x by square rooting both sides. Then isolate the x.

Answer 10

Oh But he said this: "never mind! instead do it for the equation 2x^2-x-1/x^2-4x=3"

Answer 11

Oh, didn't see that :P

Answer 12

oh ha sorry @Jhannybean

Answer 13

i have the asymptotes what about the rest?

Answer 14

especialy x's y's and hole

Answer 15

can someone just tell me the equations for each part, it would help a lot!

Answer 16

\[y=\frac{2x^2-x-1}{x^2-4x-3}\]\[\begin{align}
2x^2-x-1
\\&= x^2-x-2
\\&=(x-2)(x+1)
\\&=\left(x-\frac{2}{2}\right)\left(x+\frac{1}{2}\right)
\\&=(x-1)(2x+1)
\end{align}\] \[y=\frac{(x-1)(2x+1)}{(x-3)(x-1)}\]

Answer 17

Well,... I would set it up in that fashion to find everything that we need.

Answer 18

vertical asymptotes: just find the 0's in the denominator: \((x-3)(x-1)\)

horizontal asymptotes: compare \(\dfrac{2x^2}{x^2}\). Since the degree of the polynomials are the same, the HA = \(\dfrac{2}{1} = 2\)

No Slant.

Answer 19

awesome thanks

Answer 20

For x and y intercepts:

x-int: \(0=\dfrac{(x-1)(2x+1)}{(x-3)(x-1)}\) . Cross multiply, and solve for x-values.

y-int: \(y=\dfrac{2(0)^2-(0)-1}{(0)^2-4(0)-3}\) Solve

Answer 21

Holes:

Happen when you have a removable factor from your function:\[y=\frac{\color{red}{(x-1)}(2x+1)}{\color{red}{(x-1)}(x-3)}\] what value of x would make the denominator = 0?

Answer 22

Domain:
\[y=\frac{(x-1)(2x+1)}{(x-3)(x-1)}\]Which values of x would cause the denominator to equal 0? solve for \((x-3)(x-1)=0\)

Range: find the range by graphing your function.