To determine the value of \( k \) in the equation \( g(x) = f(x) + k \), you would typically compare the graphs of \( f(x) \) and \( g(x) \).
Here’s how you can find \( k \):
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Identify a Point on f(x): Select a specific point \( (a, f(a)) \) on the graph of \( f(x) \).
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Find the Corresponding Point on g(x): Look for the corresponding point \( (a, g(a)) \) on the graph of \( g(x) \).
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Set Up the Equation: Since \( g(x) = f(x) + k \), you can express this at the point \( x = a \): \[ g(a) = f(a) + k \]
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Solve for k: Rearranging gives: \[ k = g(a) - f(a) \]
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Substitute Values: Insert the values of \( g(a) \) and \( f(a) \) that you've identified from the graphs.
Without the specific graphs for \( f(x) \) and \( g(x) \), I can't provide a numerical value for \( k \). If you have specific values or points from the graphs of \( f \) and \( g \), please provide those, and I can help you calculate \( k \).
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