Question

Complete the missing parts of the

table for the following function.
y = ()*
X-2 -1
0 1 2 3
y 36 [?] 1 1
1
216

Answer 1

Remember the property:

a^-1 = (1/a)^1

and:

(a/b)^n = (a^n)/(b^n)

A table for a function like:

`\left[\begin{array}{ccc}x&f(x)\\&\\&\\&\\&\end{array}\right]`

Is just completed as:

`\left[\begin{array}{ccc}x&f(x)\\x_1&f(x_1)\\x_2&f(x_2)\\x_3&f(x_3)\\x_4&f(x_4)\end{array}\right]`

So, here we have:

y = f(x) = (1/6)^x

To complete the table, we need to find:

f(-1)

and

f(2)

So let's find these two values:

f(-1) = (1/6)^-1 = (6/1)^1 = 6

and the other value is:

f(2) = (1/6)^2 = 1/36

Then the complete table is:

`\left[\begin{array}{ccc}x&f(x)\\-2&36\\-1&6\\0&1\\1&1/6\\2&1/36\\1&1/216\end{array}\right]`