Question

The figure shows the graphs of the functions y=f(x) and y=g(x). the four indicated points all have integer coordinates. If g(x) = f(x) +k, what is the value of k?

Answer 1

k = -2

Explanation:

The graph clearly shows the y-intercept of f(x) as being 4, and that of g(x) as being 2. Thus, g(x) = f(x) -2 = f(x) +k.

Subtracting f(x) from that equation, you get k = -2.

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Check

g(x) is displaced 3 units to the right of f(x). The slopes of both f(x) and g(x) are 2/3, so a displacement of 3 units right is equivalent to a displacement of 2 units down. k represents the vertical translation, so is -2.