The graph of g(x) is a vertical shift of the graph of f(x) 7 units upward.
Explaining how is the graph of f(x) compare to g(x).
If g(x) = f(x) + k and the value of k is 7, it means that every y-value of g(x) is obtained by adding 7 to the corresponding y-value of f(x).
Imagine the graph of f(x) as a curve on a coordinate plane. If you add a constant value k = 7 to every y-coordinate of this curve, it's like shifting the entire graph vertically upward by 7 units.
For example, if a point on the original curve was (a, b), then on the graph of g(x) = f(x) + 7, this point would be (a, b + 7). This means that every point on the graph of g(x) is 7 units higher than its corresponding point on the graph of f(x).
So, graphically, the graph of g(x) is vertically shifted upward by 7 units compared to the graph of f(x). Therefore, the slope and shape of the graph remains the same, but all points on the graph of g(x) are 7 units higher than their corresponding points on the graph of f(x)