Unit 7, Lesson 18
Comparing Transformations
Algebra 2
18.1
Warm-up
For each pair of graphs, be prepared to describe a transformation from the graph on top to the graph on the bottom.
Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
For each pair of graphs, be prepared to describe a transformation from the graph on top to the graph on the bottom.
Here is the graph of and the graph of , which is a transformation of .
Here are graphs of two trigonometric functions:
The function is given by . How can we transform the graph of to look like the graph of ? Looking at the graph of , we need to make the period and the amplitude smaller, translate the graph up, and translate the graph horizontally so it has a minimum at .
The amplitude of is and the period is , so we can begin by changing to . The midline of is 2.5 so we need a vertical translation of 2.5, giving us . The function has a minimum when , while has a minimum when . So a horizontal translation to the right by is needed. Putting all of this together, we have an expression for : .
Another way to think about the transformation is to first notice that has a minimum when is 0. If we translate right by , then also has a minimum at . The period of is , so we can write . The amplitude of is and it's midline is 2.5, so we end up with the expression for . This is the same as , just thinking of the horizontal translation and scaling in different orders.