1. Functions, Symmetry, and the Parent Functions
Honors Precalculus
January 23 & 25, 2018
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. 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…

11. Homework: 1/25/18
Page 69 #43, 45, 69, 85, 87, 88, 95
Worksheet Provided

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