Describe how the graph of the function is related to the graph of f(x) + x^2

g(x) = x2 – 7

  g(x) is f(x) translated downward by 7 units

Step-by-step explanation:

Adding a value to a function translates its graph upward by that value. Here, -7 is added, so the graph is translated downward by 7 units.

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This should be no mystery. When (x, y) is plotted on a graph, the y-coordinate specifies the vertical distance from the x-axis. Then (x, y-7) would specify a vertical distance that is 7 units less. That is, the point would be 7 units lower than the point (x, y) on the graph.

f(x) = x²

g(x) = x² - 7

g(x) = f(x) - 7

So g is vertical translation of 7 units below f