Use the table to answer the question.

Question

x f(x) g(x)
−2 −7 −1
−1 0 0
0 1 1
1 2 2
2 9 3
Compare the functions f(x) and g(x) . At how many points do the functions intersect?

(1 point)
The functions f(x)
and g(x)
intersect at
data points

Answer 1

To determine how many points the functions $f(x)$ and $g(x)$ intersect, we need to compare their values at the given $x$ points in the table.

Let's list the points from the table:

• For $x=-2$:

  • $f(-2)=-7$
  • $g(-2)=-1$

• For $x=-1$:

  • $f(-1)=0$
  • $g(-1)=0$

• For $x=0$:

  • $f(0)=1$
  • $g(0)=1$

• For $x=1$:

  • $f(1)=2$
  • $g(1)=2$

• For $x=2$:

  • $f(2)=9$
  • $g(2)=3$

Now, let's identify the points of intersection:

• At $x=-2$: $f(-2)\ne g(-2)$
• At $x=-1$: $f(-1)=g(-1)$
• At $x=0$: $f(0)=g(0)$
• At $x=1$: $f(1)=g(1)$
• At $x=2$: $f(2)\ne g(2)$

From this, we see that the functions $f(x)$ and $g(x)$ intersect at the following points:

• $x=-1$
• $x=0$
• $x=1$

Thus, the functions intersect at 3 points.

Conclusion: The functions $f(x)$ and $g(x)$ intersect at 3 data points.