Explore transformations associated with the graphs of functions
Trigonometric transformations
The coefficient a
Write down your observations about the impact has on the graph. You may also relate the value of the coefficient with the impact. List down as many impacts as you observe.
The coefficient b
Write down your observations about the impact has on the graph. You may also relate the value of the coefficient with the impact. List down as many impacts as you observe.
The coefficient c
Write down your observations about the impact has on the graph. You may also relate the value of the coefficient with the impact. List down as many impacts as you observe.
The coefficient d
Write down your observations about the impact has on the graph. You may also relate the value of the coefficient with the impact. List down as many impacts as you observe.
Quadratic function
Now replace with and observe the impact of the coefficients on this graph. State the impact of all the coefficients below.
Any function
Create your own function for g(x), predict the impact and observe if your prediction is accurate. State your prediction and the level of accuracy below.
My conjecture
Based on this exploration, form a conjecture that lists the impact that a, b, c and d have on the function's graph. The conjecture must ensure precision, listing the impact as well as the scope of the impact. Also, list down any constraints or assumptions you may have. After listing down the conjecture, select a mathematical approach to ascertian the truth of your conjecture.