Linear or Nonlinear? Find the next 2 values in the table. Can you find the rule? If not, why?

9514 1404 393

  linear

  (x, y) = (36, 54), (68, 102)

Step-by-step explanation:

We observe that y-values are proportional to x-values with a constant of proportionality of 1.5. This is a linear function.

"The next 2 values in the table" presumes we can find the rule for choosing x. For the answer above, we have observed that first differences in x-values increase by powers of 2:

  8-6 = 2

  12 -8 = 4

  20 -12 = 8

So we have chosen the next two x-values to be 16 and 32 more than the one before:

  next x = 20 +16 = 36

  x after that = 36 +32 = 68

That is, the rule for x is ...

  xn = 4 + 2^n

and the rule for y is ...

  y = 1.5x . . . a linear function

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: