Question

h(x)=x^2/x^3-4x...how do you find the domain

Answer 1

the domain is all x's that the equation is defined
for example
the domain of x^2 is all real numbers because you can put anything in for x
the domain of 1/x is all reals except zero because you cannot divide by zero
what values can't you plug into the original equation? (things that would result in divide by zero)

Answer 2

huh

Answer 3

example
the function 1/(x+3)
what number could you plug in to make the denominator equal to zero?

Answer 4

-3

Answer 5

right
so -3 is not in the domain
all other numbers are

Answer 6

i have (-00,-2)U(2,00)..thats da infinity symbol

Answer 7

so (-3,00)?

Answer 8

and everything on the other side too
(-00,-3)U(-3,00)

Answer 9

ok so mines isnt rite for my problem

Answer 10

is the problem like this
(x^2/x^3)-4x
or like this
(x^2)/(x^3-4x)

Answer 11

(x-2)/(x^3-4x)

Answer 12

ok so what numbers would make the denominator zero?

Answer 13

2

Answer 14

and -2

Answer 15

and 0

Answer 16

so the domain is everything except those 3 numbers

Answer 17

(-00,-2)U(-2,0,2)U(2,00)?

Answer 18

close
check your notation
the middle part should be (-2,0)U(0,2)

Answer 19

why would you write it that way

Answer 20

and one more question

Answer 21

to answer your first question, its because 0 is not included, just like -2 and 2
you have to write it that way to show that 0 isnt included

Answer 22

ok

Answer 23

what's your other question?

Answer 24

how do you graph g(x)=(-√x+2)+2 without usin a calculator

Answer 25

is the first 2 under the square root?

Answer 26

yea

Answer 27

in that case, its really easy
do you know what the graph of y=sqrt(x) looks like?

Answer 28

yea but i dont know how you tie that in to the problem like how do you know which way the graph moves and wheres its suppose to be

Answer 29

y=sqrt(x)
substitute in x+2 for x moves the entire graph left 2 spaces
****IMPORTANT*****
this wouldnt be the case if it was y=sqrt(x)+2
it has to be y=sqrt(x+2)

if the number with x is positive, the graph is moved to the left
if its negative, its moved to the right

the number outside sqrt(x) tells how far up or down to move it
example
sqrt(x)+1
is moved up 1
if it was -1 instead, it would be moved down 1

a negative in front of the entire thing mirrors it over the x axis

Answer 30

back to the original
since the main part of the function is negative, it gets flipped over the x axis
a substitution of x+2 was made for x (its all in the parenthesis)
so the graph gets moved left 2 spaces
2 was added outside the parenthesis/main part)
so the graph is moved up 2 spaces
ill post a drawing