Question

Complete the table of values

Answer 1

Both problems give you a function in the second column and the x-values. To find out the values of a through f, you need to plug in those x-values into the function and simplify!

You need to know three exponent rules to simplify these expressions:
1) The negative exponent rule says that when a base has a negative exponent, flip the base onto the other side of the fraction to make it into a positive exponent. For example,
`3^(-2) = (1)/(3^(2) )`.
2) Raising a fraction to a power is the same as separately raising the numerator and denominator to that power. For example,
`((3)/(4)) ^(3) = ( 3^(3) )/(4^(3) )`.
3) The zero exponent rule says that any number raised to zero is 1. For example,
`3^(0) = 1`.


Back to the Problem:
Problem 1
The x-values are in the left column. The title of the right column tells you that the function is
`y = 4^(-x)`. The x-values are:
1) x = 0
Plug this into
`y = 4^(-x)` to find letter a:

`y = 4^(-x)\\ y = 4^(-0)\\ y = 4^(0)\\ y = 1`

2) x = 2
Plug this into
`y = 4^(-x)` to find letter b:

`y = 4^(-x)\\ y = 4^(-2)\\ y = (1)/(4^(2)) \\ y= (1)/(16)`

3) x = 4
Plug this into
`y = 4^(-x)` to find letter c:

`y = 4^(-x)\\ y = 4^(-4)\\ y = (1)/(4^(4)) \\ y= (1)/(256)`


Problem 2
The x-values are in the left column. The title of the right column tells you that the function is
`y = ((2)/(3))^x`. The x-values are:
1) x = 0
Plug this into
`y = ((2)/(3))^x` to find letter d:

`y = ((2)/(3))^x\\ y = ((2)/(3))^0\\ y = 1`

2) x = 2
Plug this into
`y = ((2)/(3))^x` to find letter e:

`y = ((2)/(3))^x\\ y = ((2)/(3))^2\\ y = (2^2)/(3^2)\\ y = (4)/(9)`

3) x = 4
Plug this into
`y = ((2)/(3))^x` to find letter f:

`y = ((2)/(3))^x\\ y = ((2)/(3))^4\\ y = (2^4)/(3^4)\\ y = (16)/(81)`

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Answers:
a = 1
b =
`(1)/(16)`
c =
`(1)/(256)`
d = 1
e =
`(4)/(9)`
f =
`(16)/(81)`