Suppose the graph of f is given describe how the graph of each function can be obtained from the graph of f?
Y=-f(x)+2
Y=3f(x)-2
To obtain the graph of each function from the graph of f, we need to apply certain transformations to f(x).
1) For the function y = -f(x) + 2:
- The negative sign "-f(x)" reflects the graph of f(x) across the x-axis. This means that the positive y-values become negative, and the negative y-values become positive.
- The "+2" shifts the reflected graph upward by 2 units. This means that every point on the original graph of f(x) will be 2 units higher on the new graph.
2) For the function y = 3f(x) - 2:
- The "3f(x)" stretches or compresses the graph of f(x) vertically by a factor of 3. This means that the y-values on the new graph will be three times larger or smaller than the corresponding y-values on the original graph.
- The "-2" shifts the vertically scaled graph downward by 2 units. This means that every point on the vertically stretched/compressed graph will be 2 units lower on the new graph.
In summary, to obtain the graph of y = -f(x) + 2, we reflect the graph of f(x) across the x-axis and shift it upward by 2 units.
To obtain the graph of y = 3f(x) - 2, we stretch or compress the graph of f(x) vertically by a factor of 3 and shift it downward by 2 units.
To obtain the graph of each function from the given graph of f, you need to perform specific transformations. Here are the steps for each function:
For the function Y = -f(x) + 2:
1. Take the graph of f and reflect it across the x-axis.
2. This reflection changes the sign of the y-values, so all the positive values of f(x) become negative, and vice versa.
3. Finally, shift the entire reflected graph vertically upward by 2 units.
For the function Y = 3f(x) - 2:
1. Begin with the graph of f.
2. Multiply all the y-values of f(x) by 3. This stretches or compresses the graph vertically depending on the value of f(x).
3. Finally, shift the entire stretched/compressed graph downwards by 2 units.
By following these steps, you can obtain the graph of each function from the given graph of f.
To obtain the graph of each function from the graph of f, we need to apply the given transformations to the original graph.
1. Y = -f(x) + 2:
This function involves taking the negative of f(x), and then adding 2 to the result. Here's how you can obtain the new graph:
- Reflect the original graph of f(x) over the x-axis to get the graph of -f(x).
- Then, shift the reflected graph 2 units upwards to obtain the final graph, Y = -f(x) + 2.
2. Y = 3f(x) - 2:
This function involves multiplying the values of f(x) by 3, and then subtracting 2 from the result. Follow these steps to obtain the new graph:
- Stretch the original graph of f(x) vertically by a factor of 3.
- Then, shift the stretched graph 2 units downwards to get the final graph, Y = 3f(x) - 2.
By applying these transformations to the graph of f, you can obtain the graphs of Y = -f(x) + 2 and Y = 3f(x) - 2.