b Use the transformations described in Part A to write the equation.
A
a Reflection across the x-axis, translation 3 units to the left, and translation 2 units up
B
b y=-sqrt(x+3)+2
Practice makes perfect
a We are asked to describe the transformations used to create the given graph. Let's start by recalling the graph of the radical parent function y=sqrt(x).
Looking at the given graph, we can see that it has been reflected across the x-axis. We can also see that it has not been stretched or compressed.
Now we only need to consider the horizontal and vertical translations. Let's compare the given graph to the graph of the reflected parent function.
The graph has been translated 3 units to the left and 2 units up.
b In order to write an equation for the given graph we will use the transformations of the radical parent function y=sqrt(x) described in Part A. Note that an equation of the transformed radical parent function has the following form.
y= asqrt(x- h)+ k
In this form each of the constants represents one of the three types of transformations. Let's determine these variables for the given graph. From Part A we know that the graph has been reflected across the x-axis, so a= - 1. It has also been translated 3 units to the left so h= - 3, and translated 2 units up so k= 2.
y= - 1sqrt(x-( - 3))+ 2
⇕
y=-sqrt(x+3)+2
Extra
Possible Transformations
The following table illustrates the general form for all possible transformations of functions.
