Sign In
A horizontal translation 4 units to the right.
A vertical shrink by a factor of 2.
A vertical translation 1 unit up.
First, we can do a reflection in the y-axis. This will transform the graph of the parent function, y=∣x∣, to the graph of y=∣-x∣. Notice that, since the graph of y=∣x∣ is symmetrical about y-axis, this will not change how it looks.
Now, let's do a horizontal translation 4 units to the right. Then the graph of y=∣-x∣ becomes y=∣-(x−4)∣.
Next, we will do a vertical shrink by a factor of 2. This transforms the graph of y=∣-(x−4)∣ to the graph of y=21∣-(x−4)∣⇔y=∣∣∣-21(x−4)∣∣∣.
Finally, we have a vertical translation 1 unit up. From y=∣∣∣-21(x−4)∣∣∣ we get the final graph, y=∣∣∣-21(x−4)∣∣∣+1.
Notice that there are many ways to obtain the graph of our function transforming the graph of its parent function. Here we considered only one of the many possibilities.
x | ∣∣∣∣∣-21x+2∣∣∣∣∣+1 | Simplify | g(x) |
---|---|---|---|
-4 | ∣∣∣∣∣-21(-4)+2∣∣∣∣∣+1 | ∣4∣+1 | 5 |
-2 | ∣∣∣∣∣-21(-2)+2∣∣∣∣∣+1 | ∣3∣+1 | 4 |
0 | ∣∣∣∣∣-21(0)+2∣∣∣∣∣+1 | ∣2∣+1 | 3 |
2 | ∣∣∣∣∣-21(2)+2∣∣∣∣∣+1 | ∣1∣+1 | 2 |
4 | ∣∣∣∣∣-21(4)+2∣∣∣∣∣+1 | ∣0∣+1 | 1 |
6 | ∣∣∣∣∣-21(6)+2∣∣∣∣∣+1 | ∣-1∣+1 | 2 |
Now we can plot these points and connect them to create our graph of g(x).