Use the Table to answer th question

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<___

Answer 1

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 \( -2 \leq x < 1 \).