Question

f(x) = (2) / (x^2-2x-3)
Graph
Domain
Range
X & Y intercepts
Horizontal & Vertical Asymptote

Answer 1

Domain: {x element R : x!=-1 and x!=3}
Range: {f element R : f<=-1/2 or fɬ}

Answer 2

@timo86m

Answer 3

domain is all x values that make it work. In other words no division by zero

find it thru this:

(x^2-2x-3)=0 solve for x. and then say domain is every real number except x=(whatever you got as answer)

Answer 4

https://www.google.com/search?q=(2)+%2F+(x%5E2-2x-3)&oq=(2)+%2F+(x%5E2-2x-3)&aqs=chrome..69i57.624j0&sourceid=chrome&ie=UTF-8
Here is your graph

Answer 5

Range is all y values that are allowable or that work.

If you look at the graph of it. You can see it is all real numbers :)

Answer 6

So it's
domain: all real numbers except x
range: all real numbers except y

Answer 7

to find y intercept make x=0: just plug in 0 at x and evaluate
(2) / (0^2-2*0-3)=-0.666

to find x intercept make y=0 i think there are non tho

Answer 8

Ohh i'm still confused

Answer 9

Find the derivative of the following via implicit differentiation:
d/dx(f(x)) = d/dx(2/(x^2-2 x-3))
Rewrite the expression: d/dx(f(x)) = d/dx(f(x)):
d/dx(f(x)) = d/dx(2/(-3-2 x+x^2))
The derivative of f(x) is f'(x):
f'(x) = d/dx(2/(-3-2 x+x^2))
Factor out constants:
f'(x) = 2 d/dx(1/(-3-2 x+x^2))
Using the chain rule, d/dx(1/(x^2-2 x-3)) = d/( du)1/u ( du)/( dx), where u = x^2-2 x-3 and ( d)/( du)(1/u) = -1/u^2:
f'(x) = 2 -(d/dx(-3-2 x+x^2))/(x^2-2 x-3)^2
Simplify the expression:
f'(x) = -(2 (d/dx(-3-2 x+x^2)))/(-3-2 x+x^2)^2
Differentiate the sum term by term and factor out constants:
f'(x) = -(2 d/dx(-3)-2 d/dx(x)+d/dx(x^2))/(-3-2 x+x^2)^2
The derivative of -3 is zero:
f'(x) = -(2 (-2 (d/dx(x))+d/dx(x^2)+0))/(-3-2 x+x^2)^2
Simplify the expression:
f'(x) = -(2 (-2 (d/dx(x))+d/dx(x^2)))/(-3-2 x+x^2)^2
The derivative of x is 1:
f'(x) = -(2 (d/dx(x^2)-1 2))/(-3-2 x+x^2)^2
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
f'(x) = -(2 (-2+2 x))/(-3-2 x+x^2)^2
Expand the left hand side:
Answer: |
| f'(x) = -(2 (-2+2 x))/(-3-2 x+x^2)^2

Answer 10

Maybe that will help =)

Answer 11

Lets do domain. Your graph/ function is a ratio. Takes the form
c/a

where c could be a function or number. In your case c is 2
where a is another function. Could be x could be x^2. in your case a is (x^2-2x-3)

now lets consider a simple case. 1/x What is its domain?

Domain is defined as all the x numbers that make the function 1/x work. Turns out all numbers except 0 work. Turns out that division by zero makes it undefined.

now your case
(2) / (x^2-2x-3)

is same and there is not division by 0

x^2-2x-3=0
(x-3) (x+1) = 0 we factored

so x= 3 and -1

Domain is all real numbers except 3 and -1

Answer 12

What's the range ?