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Sketching the Graph of a Cubic and Transformations Thereof
The mathematical solution explains how to sketch the graph of a quadratic function given one of the roots of the equation. The factor theorem is used to express the function as a product of three linear factors and hence find all three roots. The general shape of the graph can then be determined. The point of intersection of the y axis is then found before the graph is sketched.
The video then explains how to sketch the graph of y = -f(x) by reflecting in the x axis, the graph of y=2f(x): a stretch from the x axis parallel to the y axis scale factor 2 and the graph of y= f(2x): a stretch from the y axis parallel to the x axis, scale factor 0.5
Graphical solution 1 explains how to use the graphic calculator to sketch the cubic graph to verify their answer and how to adjust the scale on the axes. Graphical solution 2 explains how to use the graphic calculator to verify that the correct reflection has been drawn and how to find the points of intersection with the x axis. Graphical solution 3 explains how to use the graphics calculator to verify the graph of y=f(2x) by drawing an appropriate graph and finding the points of intersection of the graph with the axes and the value of a local minimum on the graph. Graphical solution 4 verifies the solution to drawing y= f(2x)
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