A function \( f(x) \) is a linear function and the function \( g(x)=f(x)+k \) .If the value of k is 4 , how does the graph of \( g(x) \) compare with the graph \( f(x) \) ?

When you add a constant \( k \) to a linear function \( f(x) \), like in \( g(x) = f(x) + 4 \), it shifts the entire graph of \( f(x) \) vertically upward by 4 units. So, if a point on the graph of \( f(x) \) was at (x, y), the corresponding point on the graph of \( g(x) \) will be at (x, y + 4). This means that every point moves up while the slope of the line remains unchanged, keeping the linearity intact! This transformation preserves not only the slope but also the x-intercepts. That means, if the function \( f(x) \) crossed the x-axis at some point, the function \( g(x) \) will cross the x-axis higher, creating a parallel line that retains its original angle but rises to a new height. So, in essence, think of \( g(x) \) as the jubilant sibling of \( f(x) \), just elevated by 4 units!