Suppose the graph of f is given describe how the graph of each function can be obtained from the graph of f?

Question

Y=-f(x)+2
Y=3f(x)-2

Answer 1

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.