The graph of \(y = x^2\) contains the points A(0, 0) and B(1, 1). Describe the graph of \(y = -2(x - 4)^2 + 3\), and give the coordinates of the points that correspond to A and B on the transformed graph.
Solution
\( y = -2(x - 4)^2 + 3\) would be a parabola that is flipped over the x-axis, stretched vertically by a factor of 2, moved up 3, and moved right 4. Point A would become (4, 3), and Point B would become (5, 1).
Describe the graph of \( \displaystyle y = \frac{|6 - x|}{3}\). A(0, 0) and B(1, 1) are on the graph of \(y = |x|\). What are the coordinates of the corresponding points on the transformed graph?
Solution
This would be a V, squished vertically by a factor of 3, flipped over the y axis (which doesn't make it look different) and moved to the right by 6. The vertex becomes (6, 0), and the point (1, 1) becomes \( \displaystyle \left( 5, \frac{1}{3} \right) \)
Using 2 rules, give the piecewise definition of the function whose graph is below