Changing a Coefficient - Task
This figure shows the graph of function .
Changing one of the coefficients of the the function f(x), modify this function in order to obtain functions with the properties listed below.
In each case, check the following: Can the requested property be achieved by changing the coefficient of ? of x? the free coefficient?
If possible' do it. If not' explain why.
- The graph of the modified function passes through the origin of the coordinate system.
- The graph of the modified function intersects the graph of the original function in one point only.
- The graph of the modified function intersects the graph of the original function in more than one point.
- The graph of the modified function does not intersect the graph of the original function.
- The graph of the modified function does not intersect the x-axis.
- The graph of the modified function intersects the x-axis in precisely one point.
- The modified function has a minimum.
- The axis of symmetry of the modified function is x=2.