1. Functions, Symmetry, and the Parent Functions
Honors Precalculus
January 19-20, 2016
Mrs. Agnew

2. Essential Question Essential Vocabulary
How do you find the domain of a function?
How do you determine the symmetry of a function?
Essential Vocabulary
Function Parent Function
Symmetry Domain
Even/Odd Function

3. Terminology Function: rule that assigns every x to exactly one y.
One-to-One Function?
Domain: all x values for a given relation
Range: all y values for a given relation
Four methods of representing a function: visually, algebraically, verbally, numerically
Examples: Function from graph?
Domain/Range from graph

4. Function Notation
Useful in demonstrating how to evaluate a function for a given value of x
Terminology: independent variable, dependent variable
Guided Practice
Page 69 #40 – 46 (Even), 70

5. Symmetry with Respect to X-Axis
Test for x-axis symmetry
f(x) = - f(x)
If you replace y with –y, do you
return the same equation?
Examples…
y2 = 3x – 4
|y| = 5x2 – 4
y4 = -2x + 6

6. Symmetry with Respect to Y-Axis
Test for y-axis symmetry
f(x) = f(-x)
If you replace x with –x, do you
return the same equation?
Examples…
x2 = 5y – 8
y = -3|x| + 7
y = x4 – 7x2 + 2

7. Symmetry with Respect to Origin
Test for origin symmetry
f(x) = - f(-x)
If you replace y with –y AND x with -x,
do you return the same equation?
Examples…
x4 = -3y2 + 11
x2 + y2 = 9
y = - x
Examples…

8. Graphing Using Symmetry
Symmetry can help us graph by using a graph’s “Mirror Image”
Graphing with symmetry is really reflecting a graph over the origin, x-axis, or y-axis
Examples

9. Even and Odd Functions
A function is EVEN if it is symmetric to the y-axis.
A function is ODD if it is symmetric to the origin.
What would a function be called if it were symmetric about the x-axis?
Examples…

10. Homework: 1/19/17
Page 69 #43, 45, 69, 85, 87, 88, 95
Worksheet Provided

11. Domain & Range
Recall that the domain of a function includes all of the values of x for which the function is defined.
“Problems” in Domain
Denominators
Square Roots
Range is all of the possible values for y.
Examples…

12. Parent Functions
The parent function is the “easiest” graph of a group of functions.
We will investigate parent functions for the following functions:
1. Linear Greatest Integer
2. Absolute Value 6. Reciprocal
3. Quadratic & Semicircle
Square Root 8. Exponential &
4. Cubic & Logarithmic
Cubic Root 9. Trigonometric

13. Homework: 1/20/17
Page 69 #43, 45, 69, 85, 87, 88, 95
Worksheet Provided