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.
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