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Original Question
Use the Table to answer th question x f(x) g(x) -2 -7 -1 -1 0 0 0 1 1 1 2 2 2 9 3 questions Compare the functions f(x) and g(x)...Asked by rr
Use the Table to answer th question
x f(x) g(x)
-2 -1 -1
-1 3/4 0
0 1 1
1 1 1/4 2
2 3 3
questions
Compare the functions f(x) and g(x). At how many points do the functions intersect?
f(x) is greater than or equal to g(x) when __<x<___
x f(x) g(x)
-2 -1 -1
-1 3/4 0
0 1 1
1 1 1/4 2
2 3 3
questions
Compare the functions f(x) and g(x). At how many points do the functions intersect?
f(x) is greater than or equal to g(x) when __<x<___
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To compare the functions \( f(x) \) and \( g(x) \) based on the provided table:
- For \( x = -2 \): \( f(-2) = -1 \) and \( g(-2) = -1 \) (intersection)
- For \( x = -1 \): \( f(-1) = \frac{3}{4} \) and \( g(-1) = 0 \) ( \( f(-1) > g(-1) \))
- For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) (intersection)
- For \( x = 1 \): \( f(1) = 1 \frac{1}{4} = \frac{5}{4} \) and \( g(1) = 2 \) ( \( f(1) < g(1) \))
- For \( x = 2 \): \( f(2) = 3 \) and \( g(2) = 3 \) (intersection)
### Intersection Points:
- The functions intersect at \( x = -2 \), \( x = 0 \), and \( x = 2 \). So there are **3 points** of intersection.
### When is \( f(x) \) greater than or equal to \( g(x) \)?
From the values analyzed:
- \( f(x) \) is greater than or equal to \( g(x) \) when:
- For \( x < -1 \): \( f(-2) = g(-2) \) (equal)
- Between \( -1 < x < 1 \): \( f(x) > g(x) \)
Thus, the range where \( f(x) \) is greater than or equal to \( g(x) \) is:
- \( -2 \leq x < 1 \)
### Final Answers:
1. The functions intersect at **3 points**.
2. \( f(x) \) is greater than or equal to \( g(x) \) when \( -2 \leq x < 1 \).
- For \( x = -2 \): \( f(-2) = -1 \) and \( g(-2) = -1 \) (intersection)
- For \( x = -1 \): \( f(-1) = \frac{3}{4} \) and \( g(-1) = 0 \) ( \( f(-1) > g(-1) \))
- For \( x = 0 \): \( f(0) = 1 \) and \( g(0) = 1 \) (intersection)
- For \( x = 1 \): \( f(1) = 1 \frac{1}{4} = \frac{5}{4} \) and \( g(1) = 2 \) ( \( f(1) < g(1) \))
- For \( x = 2 \): \( f(2) = 3 \) and \( g(2) = 3 \) (intersection)
### Intersection Points:
- The functions intersect at \( x = -2 \), \( x = 0 \), and \( x = 2 \). So there are **3 points** of intersection.
### When is \( f(x) \) greater than or equal to \( g(x) \)?
From the values analyzed:
- \( f(x) \) is greater than or equal to \( g(x) \) when:
- For \( x < -1 \): \( f(-2) = g(-2) \) (equal)
- Between \( -1 < x < 1 \): \( f(x) > g(x) \)
Thus, the range where \( f(x) \) is greater than or equal to \( g(x) \) is:
- \( -2 \leq x < 1 \)
### Final Answers:
1. The functions intersect at **3 points**.
2. \( f(x) \) is greater than or equal to \( g(x) \) when \( -2 \leq x < 1 \).
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