1. Worksheet KEY 1) {0, 2} 2) {–1/2} 3) No 4) Yes 5) 6) 7) k = 1 8)
2/24/2019 9:43 PM
3.4 – Parent Functions

2. 2/24/2019 9:43 PM
3.4 – Parent Functions

3. Pre–Calculus PreAP/Dual, Revised ©2015
Symmetry
Section 3.4a
Pre–Calculus PreAP/Dual, Revised ©2015
2/24/2019 9:43 PM
3.4 – Parent Functions

4. Definitions
X–Axis Symmetry is where the graph is ABOVE x–axis and is the mirror image of the graph is BELOW the x–axis
Y–Axis Symmetry is where the graph is RIGHT side of the y–axis and is the mirror image of the graph is LEFT side of the y–axis
Origin Symmetry is where the graph is symmetrical with respect to the origin. It is only symmetric if a line crosses through the origin and two points on the graph.
2/24/2019 9:43 PM
3.4 – Parent Functions

5. Example 1
Given the graph below, state the line of symmetry with respect to the x–axis, the y–axis, or the origin
2/24/2019 9:43 PM
3.4 – Parent Functions

6. Example 2
Given the graph below, state the line of symmetry with respect to the x–axis, the y–axis, or the origin
2/24/2019 9:43 PM
3.4 – Parent Functions

7. Your Turn
Given the graph below, state the line of symmetry with respect to the x–axis, the y–axis, or the origin
2/24/2019 9:43 PM
3.4 – Parent Functions

8. Symmetry Tests
To determine whether a function is odd or even, plug a negative x for every x in an equation
ODD functions are functions that are symmetric to the origin.
Think of an ODD function being OPPOSITE.
Replacing the x and y coordinates with –x and –y
EVEN functions are functions that are symmetric to the y–axis
Think of an EVEN function being EQUAL
Replacing the x coordinates with –x only.
2/24/2019 9:43 PM
3.4 – Parent Functions

9. Example 3 Given f(x) = x2 – 5, is the function even, odd, or neither?
2/24/2019 9:43 PM
3.4 – Parent Functions

10. Example 4 Given f(x) = x3 + 2x, is the function even, odd, or neither?
2/24/2019 9:43 PM
3.4 – Parent Functions

11. Example 5 Given f(x) = x3 – 1, is the function even, odd, or neither?
2/24/2019 9:43 PM
3.4 – Parent Functions

12. Your Turn
Given f(x) = |3x| + |x|, is the function even, odd, or neither?
2/24/2019 9:43 PM
3.4 – Parent Functions

13. Assignment
Pg odd
2/24/2019 9:43 PM
3.4 – Parent Functions