Question

The functions f(x) and g(x) are graphed.

((x)
4
3
2
1
6-5-4-3-2-1₁
5 2 3 4 4 4
-2
N
-3-
g(x)
1 2 3 4 5 6 x
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)=g(0) and f(0) = g(4)
Of(2)=g(0) and f(4) = g(2)
Of(2)=g(4) and f(1) = g(1)

Answer 1

The correct answer is A. f(0) = g(0) and f(2)= g(2) because these are the only points where the curves intersect in the graph, indicating where the functions have the same value.

The graph shows two curves, one for f(x) and one for g(x).

The points where the curves intersect are the points where the functions have the same value, i.e., f(x) = g(x).

In the given graph, the curves intersect at two points:

At x = 0, both f(x) and g(x) are equal to 2.

At x = 2, both f(x) and g(x) are equal to 4.

Therefore, the two points that satisfy f(x) = g(x) are (0, 2) and (2, 4).

Options B, C, and D do not hold true because:

Option B: f(2) is not equal to g(0) in the graph. At x = 0, g(x) is 2, not 0.

Option C: f(4) is not equal to g(2) in the graph. At x = 2, g(x) is 4, not 2.

Option D: f(1) is not equal to g(1) in the graph. At x = 1, f(x) is 3 and g(x) is 1.

Therefore, only option A correctly identifies the points where f(x) = g(x).

The correct option is A. f(0) = g(0) and f(2)= g(2).