Consider the following figure that shows the graph of the function F defined by
F(x) = | 2x | + 4 for all numbers x:
For which of the following functions G defined for all numbers x does the graph of G intersect the graph of F?
F(x) = |2x| + 4
Option A: G(x) = x + 3
If x > 0 or x = 0
2x + 4 = x + 3
x = -1 < 0
Therefore, this case is not possible.
If x < 0
-2x + 4 = x + 3
3x = 1
x = 1/3 > 0
Therefore, this case is not possible.
Option B: G(x) = 2x - 2
If x > 0 or x = 0
2x + 4 = 2x - 2
This case is not possible.
If x < 0
-2x + 4 = 2x - 2
x = 1.5 > 0
This case is not possible.
Option C: G(x) = 2x + 3
If x > 0 or x = 0
2x + 4 = 2x + 3
This case is not possible.
If x < 0
-2x + 4 = 2x + 3
x = 0.25 > 0
This case is not possible.
Option D: G(x) = 3x - 2
If x > 0 or x = 0
2x + 4 = 3x - 2
x = 6
This case is possible.
Therefore, the answer is option D.
Create a FREE account and get: