write a rule for the following function

Question

i need to write the rule for the following function

x=-1,0,1,2

y=1/24,1/6,2/3,2 2/3

 

Answer 1

hi Lejia,

 

if you look closely at the values of y you will see that the change from one to the next has a consistent pattern

 

each value is 4 times the previous value

 

therefore we can say that y = 4^x times some initial value(V)

 

we can find that V by substituting the x and y values at any point

 

1/6 = 4⁰ * v

 

v = 1/6

 

and our expression is

 

y = 4^x/6

 

Hope this helps

 

 

 

 

Answer 2

See if you can find a pattern in what y is doing from one x to the next.

 

What I see is that each y is 4 times the previous one.  That means it's a geometric sequence with a multiplier of 4.

 

So a function like y = a4^x is a reasonable place to start.  The question is, what is a?  Well in this equation, when x = 0, y = a.  And from the list you gave, when x = 0, y = 1/6.  So maybe a = 1/6?

 

Try it.  Does y = 4^x/6 work?