At the beginning, we drew two graphs, which intersected at two points. (secant lines) However, only at one point, the two graphs intersected at only one point (2,2). (tangent lines) While making the first graph, we knew the definition of secant and tangent lines.
What we struggled was that we had to make two graphs move at the same time to make the second graph. We could move a graph at a time but we had to move two graphs. We did not figure out how to do it, but we found the play/stop button and clicked both of the graphs to see if it worked, and it did!
The equation for the first graph was f(x)=mx-a, and the second one is f(x)=mx-ab/2. The only difference was Y-intercept. We were not sure how it did work, but we plugged in many numbers and tried a lot.
We created a totally different graph from first two ones. We set up a point at (0,0) and we tried sin graphs, natural log graphs, and power function graphs. But, anything did not satisfy our desire to create a crazy graph. We thought tangent graph looked complicated and ,to make something different, we put x^1.04. The moving graph was f(x)= tan (x^1.04). It looked like a hand of a clock crept fast, and we liked it!
Once we know that tangent point is (2,2), we can find a slope using limit as x approaches 2. After that, we can use the equation, y=m(x-x1) +y1
Below is a link to my shared drive. See Graph 1,2, and 3.
What we struggled was that we had to make two graphs move at the same time to make the second graph. We could move a graph at a time but we had to move two graphs. We did not figure out how to do it, but we found the play/stop button and clicked both of the graphs to see if it worked, and it did!
The equation for the first graph was f(x)=mx-a, and the second one is f(x)=mx-ab/2. The only difference was Y-intercept. We were not sure how it did work, but we plugged in many numbers and tried a lot.
We created a totally different graph from first two ones. We set up a point at (0,0) and we tried sin graphs, natural log graphs, and power function graphs. But, anything did not satisfy our desire to create a crazy graph. We thought tangent graph looked complicated and ,to make something different, we put x^1.04. The moving graph was f(x)= tan (x^1.04). It looked like a hand of a clock crept fast, and we liked it!
Once we know that tangent point is (2,2), we can find a slope using limit as x approaches 2. After that, we can use the equation, y=m(x-x1) +y1
Below is a link to my shared drive. See Graph 1,2, and 3.