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.