Question

Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.

f(x) = (1/3)^x ; g(x) = (1/3)^(x-2) - 4

Answer 1

The graph of g(x) is the result of shifting the graph of f(x) = (1/3)^x two units to the right and four units downward.

Step-by-step explanation:

To describe the transformation from the graph of f(x) = (1/3)^x to g(x) = (1/3)^(x-2) - 4, we need to understand how each part of the function affects its graph.

• The (x-2) in the exponent for g(x) indicates a horizontal shift. Since we are subtracting 2 from x, this shifts the graph to the right by 2 units.
• The -4 at the end of g(x) represents a vertical shift downwards of 4 units.

To sketch the graphs, start with the exponential decay graph of f(x). Then, move every point on this graph 2 units to the right to represent the x-2 transformation, and then move each point 4 units down due to the - 4. This results in the graph of g(x).