Which statement describes the graph of function g?f(x) = 2xg(x) = 2x + 3 A. The graph of g is 3 units below the graph of f. B. The graph of g is 3 units to the right of the graph of f. C. The graph of g is 3 units to the left of the graph of f. D. The graph of g is 3 units above the graph of f.
Question
Which statement describes the graph of function g?f(x) = 2xg(x) = 2x + 3 A. The graph of g is 3 units below the graph of f. B. The graph of g is 3 units to the right of the graph of f. C. The graph of g is 3 units to the left of the graph of f. D. The graph of g is 3 units above the graph of f.
Solution
D. The graph of g is 3 units above the graph of f.
Here's why:
The function f(x) = 2x is a straight line that passes through the origin (0,0) and has a slope of 2.
The function g(x) = 2x + 3 is also a straight line with the same slope of 2, but it does not pass through the origin. Instead, its y-intercept is at (0,3).
This means that every point on the graph of g is exactly 3 units above the corresponding point on the graph of f. Therefore, the graph of g is 3 units above the graph of f.
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