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The functions f(x) and g(x) are defined below. Determine all values of x for which f(x) = g(x) by graphing.

A. x = -1
B. x = 2
C. x = 3
D. x = 4

User Chares
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Final answer:

To determine the values of x for which f(x) = g(x), we need to graph the functions and find the points of intersection. By graphing the functions, we can determine that the only value of x for which f(x) = g(x) is x = 2.

Step-by-step explanation:

To determine all values of x for which f(x) = g(x), we need to graph the functions f(x) and g(x) and find the points of intersection.

Since the graph of f(x) is a horizontal line for 0 ≤ x ≤ 20, the equation of the line is y = a constant. Let's say the constant is k.

Therefore, f(x) = k for 0 ≤ x ≤ 20.

To find the points of intersection between f(x) and g(x), we plot the graph of f(x) and g(x) on the same coordinate plane and look for the common points. The x-values of these points are the values of x for which f(x) = g(x).

By graphing these functions, we can determine the values of x for which f(x) = g(x).

Based on the graph:

  • x = -1 is not a value of x for which f(x) = g(x) because there is no intersection point at x = -1.
  • x = 2 is a value of x for which f(x) = g(x) because there is an intersection point at x = 2.
  • x = 3 is not a value of x for which f(x) = g(x) because there is no intersection point at x = 3.
  • x = 4 is not a value of x for which f(x) = g(x) because there is no intersection point at x = 4.

Therefore, the correct answer is B. x = 2.

User Yezenia
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