Final answer:
The value of k affects the slope and y-intercept of the graph of g compared to the graph of f.
Step-by-step explanation:
The given function is f(x) = 2x + 3. When we have a constant multiplier k in front of the input variable, it affects both the slope and y-intercept of the graph of g. In this case, the equation for g is g(x) = 2(0.5x) + 3. The value of k in g is 0.5.
The slope of the graph is determined by the coefficient of x. For g, the slope is half of that of f because the coefficient is 0.5. A smaller value of k makes the graph less steep, and a larger value makes it steeper.
The y-intercept of the graph is determined by the constant term. In both f and g, the y-intercept is 3 because the constant term remains the same.
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