Question

Fill out the x-y chart. 11. y = log_2 x – 1 X -2 -1 O 1 2 Y C​

​ASAP!!!!

Answer 1

`\begin{array}c\cline{1-2}\vphantom{\frac12}x&y\\\cline{1-2}\vphantom{\frac12}-2&\rm DNE\\\cline{1-2}\vphantom{\frac12}-1&\rm DNE\\\cline{1-2}\vphantom{\frac12}0&\rm DNE\\\cline{1-2}\vphantom{\frac12}1&-1\\\cline{1-2}\vphantom{\frac12}2&0\\\cline{1-2}\end{array}`

Explanation:

Given equation:

`y=\log_2x-1`

To fill out the given x-y chart, substitute each given value of x into the given log equation.

The argument of a log function can only take positive arguments, so when x = -2, x = -1 and x = 0, the y-values are undefined.

The values of y for x = 1 and x = 2 are:

`\begin{aligned}x=1 \implies y&=\log_21-1\\&=0-1\\&=-1\end{aligned}`

`\begin{aligned}x=2 \implies y&=\log_22-1\\&=1-1\\&=0\end{aligned}`

Therefore, the completed x-y chart for the equation y = log₂x - 1 is:

`\begin{array}c\cline{1-2}\vphantom{\frac12}x&y\\\cline{1-2}\vphantom{\frac12}-2&\rm DNE\\\cline{1-2}\vphantom{\frac12}-1&\rm DNE\\\cline{1-2}\vphantom{\frac12}0&\rm DNE\\\cline{1-2}\vphantom{\frac12}1&-1\\\cline{1-2}\vphantom{\frac12}2&0\\\cline{1-2}\end{array}`

Note: I have used DNE for does not exist.