Answer :
To solve this question, we need to identify the [tex]$x$[/tex]-intercepts and the [tex]$y$[/tex]-intercept from the given table of values for the function [tex]\( f(x) \)[/tex].
### Step 1: Finding the [tex]$x$[/tex]-Intercepts
The [tex]$x$[/tex]-intercepts occur where the function [tex]\( f(x) \)[/tex] is equal to 0. From the table, we look for the [tex]$x$[/tex] values where [tex]$f(x) = 0$[/tex].
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -3 & 50 \\ \hline -2 & 0 \\ \hline -1 & -6 \\ \hline 0 & -4 \\ \hline 1 & -6 \\ \hline 2 & 0 \\ \hline \end{array} \][/tex]
From the table, we see that [tex]$f(x) = 0$[/tex] at [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex]. Therefore, the [tex]$x$[/tex]-intercepts are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
### Step 2: Finding the [tex]$y$[/tex]-Intercept
The [tex]$y$[/tex]-intercept occurs where [tex]\( x = 0 \)[/tex]. We look up the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex] in the table.
From the table, when [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -4 \)[/tex]. Therefore, the [tex]$y$[/tex]-intercept is [tex]\(-4\)[/tex].
### Completed Statements
- The [tex]$x$[/tex]-intercepts shown in the table are [tex]\( -2 \)[/tex] and [tex]\( 2 \)[/tex].
- The [tex]$y$[/tex]-intercept shown in the table is [tex]\( -4 \)[/tex] [tex]\(\checkmark\)[/tex].
Thus, the complete statements are:
The [tex]$x$[/tex]-intercepts shown in the table are [tex]\( \boxed{-2} \)[/tex] and [tex]\( \boxed{2} \)[/tex].
The [tex]$y$[/tex]-intercept shown in the table is [tex]\( \boxed{-4} \)[/tex] [tex]\(\checkmark\)[/tex].
### Step 1: Finding the [tex]$x$[/tex]-Intercepts
The [tex]$x$[/tex]-intercepts occur where the function [tex]\( f(x) \)[/tex] is equal to 0. From the table, we look for the [tex]$x$[/tex] values where [tex]$f(x) = 0$[/tex].
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -3 & 50 \\ \hline -2 & 0 \\ \hline -1 & -6 \\ \hline 0 & -4 \\ \hline 1 & -6 \\ \hline 2 & 0 \\ \hline \end{array} \][/tex]
From the table, we see that [tex]$f(x) = 0$[/tex] at [tex]\( x = -2 \)[/tex] and [tex]\( x = 2 \)[/tex]. Therefore, the [tex]$x$[/tex]-intercepts are [tex]\(-2\)[/tex] and [tex]\(2\)[/tex].
### Step 2: Finding the [tex]$y$[/tex]-Intercept
The [tex]$y$[/tex]-intercept occurs where [tex]\( x = 0 \)[/tex]. We look up the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex] in the table.
From the table, when [tex]\( x = 0 \)[/tex], [tex]\( f(x) = -4 \)[/tex]. Therefore, the [tex]$y$[/tex]-intercept is [tex]\(-4\)[/tex].
### Completed Statements
- The [tex]$x$[/tex]-intercepts shown in the table are [tex]\( -2 \)[/tex] and [tex]\( 2 \)[/tex].
- The [tex]$y$[/tex]-intercept shown in the table is [tex]\( -4 \)[/tex] [tex]\(\checkmark\)[/tex].
Thus, the complete statements are:
The [tex]$x$[/tex]-intercepts shown in the table are [tex]\( \boxed{-2} \)[/tex] and [tex]\( \boxed{2} \)[/tex].
The [tex]$y$[/tex]-intercept shown in the table is [tex]\( \boxed{-4} \)[/tex] [tex]\(\checkmark\)[/tex].
