In mathematics, we will have situation to graph a function from the parent function using transformation.
Let us see, how to graph the functions which are in the form
y = af[k(x-d)] + c
using transformation with an example.
Example :
Sketch the graph of the function given below.
Solution :
The function is a transformed square root function.
So, the parent function is y = √x.
Let us look at each part of the function and write down all the transformations which we need to apply.
First, let us divide the x- coordinates of points on y = √x by 2 to compress the graph horizontally by the factor 1/2.
When we do as said above, we will get the following table of values and graph.
Let us multiply the y-coordinates of y = √(2x) by 3 to stretch the graph vertically by the factor 3.
When we do as said above, we will get the following table of values and graph.
Let us flip the graph of y = 3√(2x) over the x-axis.
(Because, we have negative sign in front of 3 in the given function)
When we do as said above, we will get the following table of values and graph.
I did both shifts together. I subtracted 4 from each of the x-coordinates and subtracted 1 from each of the y-coordinates of the graph of y = -3√(2x).
When we do as said above, we will get the following table of values and graph.
Translate the graph of y = -3√(2x), 4 units left and 1 unit down in order to get the graph of the given function
y = -3[√(2x+4)] - 1
The graph of the given function y = -3[√(2x+4)] - 1 is given in black color.
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Apr 01, 23 11:43 AM
Mar 31, 23 10:41 AM
Mar 31, 23 10:18 AM