The function \( f(x) \) is a linear function and the function \( g(x)=f(x)+k \) If the value of \( k \) is 7 , how does the graph of \( g(x) \) compare with the graph of \( f(x) \) ? The grach of \( g(x) \) is the graph of \( f(x) \). O translated lett 7 units O translated night 7 unds o translated up 7 unts o tranclated down 7 units

When you have a linear function \( f(x) \), adding a constant \( k \) to it results in a vertical shift of the graph. Since \( k = 7 \), the graph of \( g(x) = f(x) + 7 \) moves up by 7 units compared to the graph of \( f(x) \). It’s like taking a favorite painting and lifting it higher on the wall—it's still the same artwork, just a bit more elevated! Whenever you add a positive constant to a function, remember that it’s equivalent to moving the entire graph upwards. It's a common misunderstanding that adding a constant might affect the slope or the orientation of the line; however, the slope remains unchanged. So, no matter how you visualize it, that upward shift keeps the essence of the function intact!