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Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does f(x) + g(x) = 0 ?
- a)−3
- b)−2
- c)−1
- d)0
Correct answer is option 'B'. Can you explain this answer?
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Graphs of the functions f and g are shown in the xy-plane above. For w...
Choice B is correct. For any value of x, say x = x0, the point (x0, f(x0)) lies on the graph of f and the point (x0, g(x0)) lies on the graph of g. Thus, for any value of x, say x = x0, the value of f(x0) + g(x0) is equal to the sum of the y-coordinates of the points on the graphs of f and g with x-coordinate equal to x0. Therefore, the value of x for which f(x) + g(x) is equal to 0 will occur when the y-coordinates of the points representing f(x) and g(x) at the same value of x are equidistant from the x-axis and are on opposite sides of the x-axis. Looking at the graphs, one can see that this occurs at x = −2: the point (−2, −2) lies on the graph of f, and the point (−2, 2) lies on the graph of g. Thus, at x = −2, the value of f(x) + g(x) is −2 + 2 = 0.
Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, f(x) + g(x) = 0.
Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, f(x) + g(x) = 0.
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Graphs of the functions f and g are shown in the xy-plane above. For w...
Choice B is correct. For any value of x, say x = x0, the point (x0, f(x0)) lies on the graph of f and the point (x0, g(x0)) lies on the graph of g. Thus, for any value of x, say x = x0, the value of f(x0) + g(x0) is equal to the sum of the y-coordinates of the points on the graphs of f and g with x-coordinate equal to x0. Therefore, the value of x for which f(x) + g(x) is equal to 0 will occur when the y-coordinates of the points representing f(x) and g(x) at the same value of x are equidistant from the x-axis and are on opposite sides of the x-axis. Looking at the graphs, one can see that this occurs at x = −2: the point (−2, −2) lies on the graph of f, and the point (−2, 2) lies on the graph of g. Thus, at x = −2, the value of f(x) + g(x) is −2 + 2 = 0.
Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, f(x) + g(x) = 0.
Choices A, C, and D are incorrect because none of these x-values satisfy the given equation, f(x) + g(x) = 0.
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Graphs of the functions f and g are shown in the xy-plane above. For which of the following values of x does f(x) + g(x) = 0 ?a)−3b)−2c)−1d)0Correct answer is option 'B'. Can you explain this answer?
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