Question

H(t)=4-t^2/2-t .. find the domain and sketch the graph .. how to do this?

Answer 1

\[H(t)=4-t^2/2-t\]

Answer 2

very similar to your last question, where u stuck ?

Answer 3

i ogt stuck again :/

Answer 4

did u try to complete the square ?

Answer 5

what do you think the domain should be?
any critical thought?

Answer 6

x should not be 2 ??

Answer 7

i tried but it didnt work

Answer 8

oh, is the question:
\(\huge \frac{4-t^2}{2-t}\) ?

Answer 9

yes

Answer 10

then factor 4-t^2
can u ?

Answer 11

You are right...x should not be 2...then?

Answer 12

\(\huge use\quad a^2-b^2 = (a+b)(a-b)\)

Answer 13

(2+t) (2-t)

Answer 14

so now u can cancel 2-t from numerator and denominator, isn't it ?

Answer 15

yup

Answer 16

so your function is ?

Answer 17

so H(t)= (2+t)

Answer 18

\[(-\infty,0] U (2,+\infty)\]

Answer 19

is the domain correct ?

Answer 20

yes, thats the simplification of H(t)
and its the straight line , which u can plot, right ?
the domain is the values that x can take.
x cannot be =2 as denom = 0
so it will be excluded from domain.
why 0 to 2 cannot be in domain ?

Answer 21

domain \((-\infty,2) U (2,+\infty)\)

Answer 22

oh i see.. got it.. what about the graph?

Answer 23

the graph will be same as that of line y= 2+x
can u plot that ?

Answer 24

i am getting (0,2) and (-2,0) .. is this correct??

Answer 25

those intercepts are absolutely correct!

Answer 26

You just normally draw a y=2+x graph w/o x=2 point

Answer 27

now just draw a line joining them

Answer 28

is it correct ?

Answer 29

No.

Answer 30

The slope of the line on your graph is -1.

Answer 31

Consider when x=0 and y=0

Answer 32

u plotted -2,0 and 0,-2 instead

Answer 33

plot (0,2) and (-2,0)

Answer 34

where is 0,2 ??

Answer 35

When x=0, y=0+2 so (0,2) a point
When y=0, x+2=0, x=-2, so (-2,0) a point

Answer 36

0,2 means
x-co-ordinate is 0 --->point on y-axis
+2 ---->2 units UP

Answer 37

is this one correct ??

Answer 38

now that is correct!

Answer 39

now just exclude the point x=2 from your graph, because it does not belong to domain of the function

Answer 40

how do i do that ?

Answer 41

just mark a small open circle when x=2