Question

Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (a) Shift 3 units upward. (b) Shift 3 units downward (c) Shift 3 units to the right.

Answer 1

To shift a graph upward, add to the y-coordinate of each point. To shift a graph downward, subtract from the y-coordinate of each point. To shift a graph to the right, subtract from the x-coordinate of each point.

Step-by-step explanation:

To shift the graph of f upward by 3 units, we need to add 3 to the y-coordinate of each point on the graph. So, if the original equation of f is y = f(x), then the new equation for the shifted graph is y = f(x) + 3.

To shift the graph of f downward by 3 units, we need to subtract 3 from the y-coordinate of each point on the graph. So, if the original equation of f is y = f(x), then the new equation for the shifted graph is y = f(x) - 3.

To shift the graph of f to the right by 3 units, we need to subtract 3 from the x-coordinate of each point on the graph. So, if the original equation of f is y = f(x), then the new equation for the shifted graph is y = f(x - 3).

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