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)
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.
To obtain the graph of -f(x), you would start with the graph of f(x) and then reflect it across the x-axis. This means that each point on the graph of f(x) will have the same x-coordinate, but the y-coordinate will be negated.
To obtain the graph of 1/2f(x), you would start with the graph of f(x) and then vertically stretch it by a factor of 1/2. This means that each point on the graph of f(x) will have the same x-coordinate, but the y-coordinate will be halved. The graph of 1/2f(x) will be "flatter" than the graph of f(x), but it will still preserve the shape and direction of the original graph.
To obtain the graph of -f(x), you can simply take the graph of f(x) and reflect it upside down (or multiply the y-values by -1). This means that each point on the graph of f(x) will have the same x-coordinate but a y-coordinate that is the opposite sign.
To obtain the graph of 1/2f(x), you can take the graph of f(x) and shrink it vertically by a factor of 2. This means that each point on the graph of f(x) will have the same x-coordinate, but the y-coordinate will be half of its original value.
In summary:
- To graph -f(x), reflect the graph of f(x) upside down.
- To graph 1/2f(x), shrink the graph of f(x) vertically by a factor of 2.