They asked you how to transform graph of y=x^2 function to graph of y=(x-3)^2 function.frozenbananas said:im just totally confused with what the question is asking. i mean i know how to graph y=(x-3)^2 bit idk what the y=x^n is about. thanks so much!
n.karthick said:They want you to start up with graph of y=x^2 and get y=(x-3)^2, which is just shifted in x axis.
The basic process for graphing a function by transforming a graph of a function form involves identifying the parent function and the specific transformation(s) that need to be applied, such as shifting, reflecting, or stretching the graph. Then, using the coordinates of key points on the parent function, the transformed points can be plotted to create the new graph.
The direction of a graph's shift depends on the sign of the transformation value. For example, a positive value for a horizontal shift will move the graph to the right, while a negative value will move it to the left. Similarly, a positive value for a vertical shift will move the graph up, while a negative value will move it down.
Yes, multiple transformations can be applied to a graph to move it in multiple directions. Just remember to follow the order of operations, starting with horizontal shifts, then vertical shifts, followed by any reflections or stretches.
One way to easily identify key points on the parent function is to use a table of values. Plug in a few x-values and solve for the corresponding y-values, then use those coordinates to plot the points on the graph. These points can then be used as a reference for applying transformations.
The general rule for graphing by transformations is to start with the parent function and then apply the desired transformations in a specific order. Horizontal shifts are applied first, followed by vertical shifts, then any reflections, and finally any stretches. Remember to use key points from the parent function to plot the transformed points and create the new graph.