If you mean that "y-scaling" = vertical stretch/shrink, then I would consider the first part as incorrect. The way I've learned it, you can only have a vertical stretch/shrink by a positive number factor (ie. "vertical stretch by a factor of 4," "vertical shrink by a factor of 1/2"). The negative in front of the 1/3 indicates another transformation. What is it?Bugsy23 said:Homework Statement
Explain how the parabola that is the graph of f can be obtained from the graph of y=x2
Homework Equations
f(x)=-1/3(x-2)2+3
The Attempt at a Solution
a y-scaling with factor -1/3
a horizontal translation by 2 units to the right
a vertical translation by 3 units upwards
Can someone tell me if that's right or not? Thanks
Scalings and translations are mathematical transformations that are applied to a graph to change its size and position. Scaling changes the size of the graph, while translation moves the graph to a different position on the coordinate plane.
Scalings and translations do not change the shape of a graph, only its size and position. The shape of the graph remains the same, but it may appear larger or smaller and shifted to a different location on the coordinate plane.
Scaling involves multiplying the coordinates of each point on a graph by a constant value, while translation involves adding or subtracting a constant value to the coordinates of each point on a graph. Scaling changes the size of the graph, while translation changes its position on the coordinate plane.
Yes, multiple scalings and translations can be applied to a graph. The order in which they are applied can affect the final result. For example, if a scaling is applied first, followed by a translation, the graph will be both shifted and resized. However, if the order is reversed, the scaling will be based on the original position of the graph, resulting in a different final graph.
Scalings and translations are useful in graphing because they allow us to manipulate and transform a graph to better understand its features. They can also help us compare different graphs by scaling them to the same size or translating them to the same position. In real-world applications, scalings and translations can be used to analyze data and make predictions based on the trends shown in the graph.