Question

Suppose the graph of f is given describe how the graph of each function can be obtained from the graph of f?
-f(x)
1/2f(x)

Answer 1

To obtain the graph of -f(x), you would take the graph of f and reflect it across the x-axis. This means that any point (x, y) on the graph of f will become (x, -y) on the graph of -f.

To obtain the graph of 1/2f(x), you would take the graph of f and stretch it vertically by a factor of 1/2. This means that any point (x, y) on the graph of f will become (x, (1/2)y) on the graph of 1/2f. This will make the graph of 1/2f narrower and closer to the x-axis compared to the original graph of f.