Question

If x = -2 is a solution to the equation f(x) = g(x), which of these statements must be true?

a. The graphs of f and g intersect each other at x = -2.
b. The graphs of f and g intersect each other at x = 2.
c. The graphs of f and g intersect the x-axis at -2.
d. The graphs of f and g intersect the y-axis at -2.

Answer 1

If x = -2 is a solution to the equation f(x) = g(x), then the graphs of f and g intersect each other at x = -2. This indicates that both functions have the same value at x = -2, thus showing where they cross on the graph.

Correct option is A

Step-by-step explanation:

If x = -2 is a solution to the equation f(x) = g(x), this means that the graphs of f and g intersect each other at x = -2. Therefore, the correct statement is:

• The graphs of f and g intersect each other at x = -2.

This is because finding a solution to the equation f(x) = g(x) means identifying a point where the two functions have the same value, hence where their graphs cross. This point of intersection lies on the x-coordinate given by the solution, so if x = -2 is a solution, then the graphs intersect at the point (-2, f(-2)) = (-2, g(-2)).

The other options are incorrect because the intersection of graphs' reference is given in x-coordinates, not y-coordinates, and the fact that x = -2 as a solution tells us nothing about the y-intercept of either graph.