Comparing Shapes of Functions Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
1 of 51 of 5 Items
Question
Use the table to answer the 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.
Remaining Attempts : 3
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Answer 1

To determine the number of points at which the functions $f(x)$ and $g(x)$ intersect, we need to compare their values for the same $x$ in the table provided.

Here are the values from the table:

| $x$ | $f(x)$ | $g(x)$ | |---------|------------|------------| | -2 | -7 | -1 | | -1 | 0 | 0 | | 0 | 1 | 1 | | 1 | 2 | 2 | | 2 | 9 | 3 |

Now, we look for points where $f(x)=g(x)$:

• At $x=-2$: $f(-2)=-7$ and $g(-2)=-1$ (not equal)
• At $x=-1$: $f(-1)=0$ and $g(-1)=0$ (equal)
• At $x=0$: $f(0)=1$ and $g(0)=1$ (equal)
• At $x=1$: $f(1)=2$ and $g(1)=2$ (equal)
• At $x=2$: $f(2)=9$ and $g(2)=3$ (not equal)

From the analysis, the two functions intersect at the following $x$ values:

• $x=-1$
• $x=0$
• $x=1$

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