Reflection
Introduction
In this activity, you are going to be studying the effect of a reflection on the graph of a function. We chose quadratic functions for this, but this will work with all functions.
Reflection, part 1
Description
The graph of g is a transformation of the graph of g. Describe this geometric transformation.
Checking values
In the table below, you can see some values we captured from both functions. Compare them.
Compare!
Look closely to the expression of f. Describe how this expression was changed to get the expression of g.
Algebraic expression
Write down g(x) in terms of f(x).
Confirm your answers with a different function!
Reflection, part 2
On the previous questions, you saw a type of reflection. Now, we are going to learn about the second type of reflection.
Another mirror
Description
The graph of g is a transformation of the graph of g. Describe this geometric transformation.
Compare!
Compare both algebraic expressions. Describe how the expression of f was changed into the expression of g.
Checking values
In the table below, we are comparing the y-coordinates, that is, when each function reaches a certain y value. Choose a certain y-coordinate, what do you notice about the x-coordinates?
Algebraic expression
Write down g(x) in terms of f(x).