Let's carefully determine the [tex]$x$[/tex]-intercepts and [tex]$y$[/tex]-intercept from the given table.
### Determining the [tex]$x$[/tex]-intercepts:
The [tex]$x$[/tex]-intercepts occur where the function [tex]$f(x)$[/tex] equals zero (i.e., [tex]$f(x) = 0$[/tex]). We need to identify the points from the table that satisfy this condition.
From the table:
- At [tex]$x = -3$[/tex], [tex]$f -3 = 50$[/tex]
- At [tex]$x = -2$[/tex], [tex]$f(-2) = 0$[/tex]
- At [tex]$x = -1$[/tex], [tex]$f(-1) = -6$[/tex]
- At [tex]$x = 0$[/tex], [tex]$f(0) = -4$[/tex]
- At [tex]$x = 1$[/tex], [tex]$f(1) = -6$[/tex]
- At [tex]$x = 2$[/tex], [tex]$f(2) = 0$[/tex]
We find that [tex]$f(-2) = 0$[/tex] and [tex]$f(2) = 0$[/tex]. Therefore, the [tex]$x$[/tex]-intercepts are:
[tex]\[ (-2, 0) \quad \text{and} \quad (2, 0) \][/tex]
### Determining the [tex]$y$[/tex]-intercept:
The [tex]$y$[/tex]-intercept occurs where [tex]$x$[/tex] equals zero (i.e., [tex]$x = 0$[/tex]). We need to identify the point from the table that satisfies this condition.
From the table, at [tex]$x = 0$[/tex]:
[tex]\[ f(0) = -4 \][/tex]
Therefore, the [tex]$y$[/tex]-intercept is:
[tex]\[ (0, -4) \][/tex]
### Final Statements:
- The [tex]$x$[/tex]-intercepts shown in the table are [tex]\(( -2, 0 ) \quad \text{and} \quad (2,0)\)[/tex].
- The [tex]$y$[/tex]-intercept shown in the table is [tex]\(( 0, -4 )\)[/tex].
Therefore, the correct completion of the statements would be:
"The [tex]$x$[/tex]-intercepts shown in the table are [tex]$(-2, 0)$[/tex] and [tex]$(2, 0)$[/tex]. The [tex]$y$[/tex]-intercept shown in the table is [tex]$(0, -4)$[/tex]."
