Activity 5.2 Reflections and Symmetry
Overview:
Students are given a table of values for a function and asked to complete the table with values of
reflections. They are then asked to graph the original function and compare it to the transformed
functions’ graphs and to describe the relationship between the original function’s graph and the
transformed functions’ graphs.
Estimated Time Required:
The activity should take approximately 15 minutes.
Technology: None
Prerequisite Concepts:



Reflection across the x- or y-axis
Symmetry
Algebraic and geometric descriptions of even and odd functions
Discussion:
Most difficulties that students have with this material can be traced to their knowledge of function
notation. Have students complete the table and emphasize the difference between inputs and
outputs. For example, show them that g(2) = f(–2) = 12 and remind them that 2 is the input into g,
–2 is the input into f, and 12 is the output in both cases.
Activity 5.2 Reflections and Symmetry
1. Complete the table:
x
f(x)
-3
2
-2
4
-1
6
0
8
1
10
f(–x)
–f(x)
2. Letting g(x) = f(–x) and h(x) = – f(x), graph f, g, and h on the same set of axes.
3. What is the relationship between the graphs of f and g?
Between f and h?
2
12
3
14
4
16