Question

Could the table below give points on the graph of a function y = ab, for constants a and b? If so, find the function. If the table cannot represent the graph of a function y = ab, enter NA. Note that "y=" is already provided. Do not include this in your submitted response to this question. Ixl Edit

Answer 1

To find out whether this table satisfies the function y=abx. We will first find out the values of 'a' and 'b' by using any two values from the table and after obtaining full function using these points we will see whether remaining points satisfies the obtained function or not.If remaining points satisifies the obtained function then this function satisfies all the values given in the table and is valid.

Let start with values given in any two columns of the table-:

Consider function y=abx and put value in the second column from the table i.e., x=2 and y=1 in the function.

1=ab2 => a=1/b2   -------------->(1)

Now put values in the second column i.e.,x=2 and y=1

9=ab4 => a=9/b4 --------------->(2)   

Equating equation 1 and 2

1/b2 = 9/b4

  1/b2 =1/9

  1/b = 1/3. hence, b=3 and a=1/b2 = 1/9

so,our function is  y=(1/9)*(3)x --------->(3)

Now we will see whether obtained function or equation 3 satisfies remaining values present in the table.

-> Let's start with value in the first column x=0 and y=0,

=> 0=(1/9)*(3)0 = 1/9. But 0 is not equal to 1/9,Hence this value does not satisfy our obtained function.

-> Now let's try the value present in the last column x=6 and y=81

=>81=(1/9)*(3)6 = (1/9)*729 = 81.Hence, it satisfies the obtained function.

So, the final answer will be NA as value x=0 and y=0 does not satisfy our obtained function which means that our whole table cannot be represented by that function.