Question

Complete the missing parts of the table for the following function

Answer 1

The missing parts of the table for
`\( x = 0 \)` and
`\( x = 3 \)` are 1 and 216, respectively.

Let's solve for the missing values step by step.

The function given is
`\( y = 6^x \)`. This means that for each value of
`\( x \)`,
`\( y \)` will be
`\( 6 \)` raised to the power of
`\( x \)`.

Step 1: Solve for
`\( y \)` when
`\( x = 0 \)`

The exponent law states that any number raised to the power of 0 is 1. Therefore:

`\( y = 6^0 = 1 \)`

Step 2: Solve for
`\( y \)` when
`\( x = 3 \)`

To find
`\( y \)` when
`\( x = 3 \)`, we simply raise 6 to the power of 3:

`\( y = 6^3 = 6 * 6 * 6 = 216 \)`

So, the completed table should look like this:

`$\begin{array}{rrrrrrr}x & -2 & -1 & 0 & 1 & 2 & 3 \\ y & (1)/(36) & (1)/(6) & 1 & 6 & 36 & 216\end{array}$`

Answer 2

Explanation:

equation y =
`6^(x)`

When x = -1

y =
`6^(-1)` =
`(1)/(6)` (Answer)

When x = 0,

y =
`6^(0)` = 1 (Answer)

When x = 3,

y =
`6^(3)` = 216 (Answer)