Question

Rational Functions?

Answer 1

try this see if it helps! :)
http://www.purplemath.com/modules/grphrtnl.htm

Answer 2

the parent function is \(\large z(x) = \frac{a}{x}\)

Answer 3

see that the new funciton shown in graph is passing thru \(\large (\frac{1}{2}, \frac{2}{7})\)

Answer 4

plug them above and find the value of \(a\)

Answer 5

\(\large z(x) = \frac{a}{x}\)

\(\large\frac{2}{7} = \frac{a}{1/2}\)

solve \(a\)

Answer 6

\[a \div 1/2\] and then multiply both sides by 1/2?

Answer 7

yup ! that will work

Answer 8

So a = 1/7?

Answer 9

Correct!

just plugin a value in \(z(x)\)

Answer 10

the required function wud be ?

Answer 11

Umm, plugging in a number for x so z(2) = 1/7?

Answer 12

\(\large z(x) = \frac{a}{x}\)

\(\large z(x) = \frac{1/7}{x}\)

\(\large z(x) = \frac{1}{7x}\)

Answer 13

or would it be z(x) = 1/7?

Answer 14

thats the equation of shown graph \(\large z(x) = \frac{1}{7x}\)

Answer 15

How did you get 1/7x?

Answer 16

you tell me :)

Answer 17

I see that a = 1/7, but I'm not sure how you got the 7 to connect to the x

Answer 18

multiply by 7?

Answer 19

think a bit and see if u can explain how we got 7x in the bottom :)

Answer 20

yes !!

Answer 21

How come we do that?

Answer 22

we can do anything, as long as we do it to both top/bottom

Answer 23

so we multiplied by 7/7 correct?

Answer 24

thats right

Answer 25

Okay c: Can we do another one like this?

Answer 26

sure :)

Answer 27

I can make another question so you can get another medal for it if you'd like ^_^

Answer 28

dont wry about them lol, u may as here its okay

Answer 29

Okey doke!

Answer 30

the graph has a vertical asymptote at x=3

Answer 31

wat that means is the bottom goes 0, when x = 3

so, the equation will be :

\(\large y = \frac{a}{x-3}\)

Answer 32

So the equation I should start with is y = a/something right?

Answer 33

yes

Answer 34

And then I put x there automatically so its y = a/x
Now is it always going to be "-" something or will it vary?

Answer 35

have a look at graph,
its going thru point \((7, -2)\), right ?

Answer 36

Right

Answer 37

plug them in the above equation and find teh value of \(a\)

Answer 38

\(\large y = \frac{a}{x-3}\)

\(\large -2 = \frac{a}{7-3}\)

solve \(a\)

Answer 39

oh

-2 = a/ 7 -3
-2 = a/4
*4 *4
-8 = a

Answer 40

Correct ! plug that a back into the equation

Answer 41

the equation of given graph wud be :-

\(\large y = \frac{a}{x-3}\)

\(\large y = \frac{-8}{x-3}\)

Answer 42

Do I plug in for x and 7 or leave them alone?

Answer 43

x and y*

Answer 44

we're done. thats the final equation of greaph ":)

Answer 45

ohh, hmm, okay, the dotted line that goes through 3 on the x-axis, is that the vertical asymptote?

Answer 46

yes thats the vertical asymptote , where the function behaves crazily
it goes positive infinity from left,
and negative infinity from right side

Answer 47

Left and ride side meaning on the x axis right?

Answer 48

yes !

Answer 49

Okay:D Thank you! If I have any more problems can I tag you? If not it's okay xD I know how annoying tagging can be :b

Answer 50

not at all, im happy to assist a brilliant friend like u. tag me for sure when u need a helping hand :)

Answer 51

Awesome! Thank you:DD

Answer 52

np :D