Another day, another thing to add to my knowledge of derivatives. What I learned in this activity is how transformations affect the tangent line at a point. While doing the worksheet, I noticed how sometimes how the slope would change. I found that the slope would change when there were reflections over the x-axis and vertical stretches. When there was a shift, whether it was vertical or horizontal, the slope wouldn't change. I found this out by finding the derivatives of the functions and seeing the pattern.
While the worksheet mainly used square roots, I believe that this idea would work for all types of functions. I know that the way vertical stretches and compresses, vertical shifts, and horizontal shifts affects regular functions, square roots, and absolute functions the same. Let's take f(x)=2x. If you add a vertical stretch of 2, the slope is different. But when you add a vertical shift of 3, the slope stays the same. I can concur that the same rules applies to all types of functions. After discovering these patterns, it should be easier to find the tangent lines and derivatives due to knowing this pattern.
After trying the composite function on the worksheet in class, we found it too confusing to write about here. Also I am too lazy and busy to write about it.
This pattern will be very useful to know for the future.
While the worksheet mainly used square roots, I believe that this idea would work for all types of functions. I know that the way vertical stretches and compresses, vertical shifts, and horizontal shifts affects regular functions, square roots, and absolute functions the same. Let's take f(x)=2x. If you add a vertical stretch of 2, the slope is different. But when you add a vertical shift of 3, the slope stays the same. I can concur that the same rules applies to all types of functions. After discovering these patterns, it should be easier to find the tangent lines and derivatives due to knowing this pattern.
After trying the composite function on the worksheet in class, we found it too confusing to write about here. Also I am too lazy and busy to write about it.
This pattern will be very useful to know for the future.