To determine the [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-intercepts of the function [tex]\(f(x)\)[/tex] that corresponds to the given table of points, we must identify where the graph of the function crosses the [tex]\(x\)[/tex]-axis and [tex]\(y\)[/tex]-axis.
1. Finding the [tex]\(y\)[/tex]-intercept(s): The [tex]\(y\)[/tex]-intercept(s) occur where [tex]\(x = 0\)[/tex].
- From the table, the point where [tex]\(x = 0\)[/tex] is [tex]\((0, -7)\)[/tex].
Therefore, the only [tex]\(y\)[/tex]-intercept is [tex]\((0, -7)\)[/tex].
2. Finding the [tex]\(x\)[/tex]-intercept(s): The [tex]\(x\)[/tex]-intercept(s) occur where [tex]\(y = 0\)[/tex].
- From the table, the point where [tex]\(y = 0\)[/tex] is [tex]\((3, 0)\)[/tex].
Therefore, the only [tex]\(x\)[/tex]-intercept is [tex]\((3, 0)\)[/tex].
Given this information:
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -7)\)[/tex].
- The [tex]\(x\)[/tex]-intercept is [tex]\((3, 0)\)[/tex].
Thus, the correct selections are:
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -7)\)[/tex].
- The [tex]\(x\)[/tex]-intercept is [tex]\((3, 0)\)[/tex].
Incorrect statements from the choices would include:
- The [tex]\(y\)[/tex]-intercepts are [tex]\((0, -7)\)[/tex] and [tex]\((3, 0)\)[/tex]. (This statement is incorrect because [tex]\((3, 0)\)[/tex] is the [tex]\(x\)[/tex]-intercept, not a [tex]\(y\)[/tex]-intercept.)
- The [tex]\(x\)[/tex]-intercept is [tex]\((0, -7)\)[/tex]. (Incorrect because [tex]\((0, -7)\)[/tex] is the [tex]\(y\)[/tex]-intercept.)
- The 9-intercept is [tex]\((3, 0)\)[/tex]. (There is no such thing as a 9-intercept in this context.)
So, the correct answers are:
- The [tex]\(y\)[/tex]-intercept is [tex]\((0, -7)\)[/tex].
- The [tex]\(x\)[/tex]-intercept is [tex]\((3, 0)\)[/tex].
