Use the principles of translating and reflecting to graph the function
f(x)=(x-5)^3 +2
just take the graph of y=x^3 and shift it right 5 and up 2.
To graph the function f(x) = (x-5)^3 + 2 using translation and reflection principles, we can follow these steps:
1. Start by plotting the graph of the parent function f(x) = x^3. This is the basic cubic function.
2. Apply the translation principle to shift the graph 5 units to the right. To do this, take each point on the parent function and move it horizontally 5 units to the right. So if we have a point (x, y) on the parent function, the corresponding point on the translated graph would be (x+5, y).
3. Now we have the graph of f(x) = (x-5)^3, which represents shifting the cubic function 5 units to the right.
4. Finally, we apply the reflection principle by reflecting the graph across the x-axis. To reflect a point (x, y) across the x-axis, we keep the x-coordinate the same but change the sign of the y-coordinate. So, for every point (x, y) on the graph, the corresponding point on the reflected graph would be (x, -y).
5. Now we have the graph of the function f(x) = (x-5)^3 reflected across the x-axis.
6. Lastly, add 2 to the y-coordinate of each point on the graph to shift the graph upward by 2 units. So if we have a point (x, y) on the graph, the corresponding point on the final graph would be (x, y+2).
By following these steps, you can plot the graph of the function f(x) = (x-5)^3 + 2 using translation and reflection principles.