a Compare the given graph to the graph of the parent function, y=|x|.
B
b Start by reflecting the graph across the y-axis.
A
a Reflection across the x-axis, translation 2 units up, and translation 3 units to the right
B
b
Practice makes perfect
a We are asked to determine which translations of the parent function y=|x| took place to obtain the given graph. Let's recall the graph of the parent function, y=|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 2 units up and 3 units to the right.
b We will draw the graph of the transformed function after reflecting it across the y-axis and translating it 4 units down. Let's start by reflecting the graph across the y-axis. This is achieved by changing the sign of every input value.
Next we will translate the graph 4 units down. This means decreasing the value of the function by 4 for every input value.
We have obtained the graph of the transformed function after reflecting it across the y-axis and translating it 4 units down.
