Today in Pre-Calculus Go over homework Need a calculator Review Chapter 3 Homework.
Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.
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Transcript of Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.
![Page 1: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/1.jpg)
Today in Pre-Calculus
• Go over homework• Notes: Symmetry
– Need a calculator
• Homework
![Page 2: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/2.jpg)
1. Vertical: x = -3 Horizontal: none
2. Vertical: x =-2, x = 2 Horizontal: y=0
3. Vertical: x = 3 Horizontal: y =0
4. lim ( ) 5, lim ( ) 5x x
f x f x
9. lim ( ) 4, lim ( ) 4x x
f x f x
8. lim ( ) , lim ( ) 0x x
f x f x
7. lim ( ) 7, lim ( ) 0x x
f x f x
6. lim ( ) 1, lim ( ) 1x x
f x f x
![Page 3: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/3.jpg)
Symmetry• Symmetry with respect to the y-axis.
• These are EVEN functions
• Their graphs appear the same on both sides of the y-axis.
• Algebraically for every x in the domain of f , f(-x)=f(x)
![Page 4: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/4.jpg)
Symmetry• Symmetry with respect to the x-axis.
• Note: These are NOT functions
• Their graphs appear the same on both sides of the x-axis.
• Algebraically for every (x,y) on the graph (x,-y) is also on the graph.
![Page 5: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/5.jpg)
Symmetry• Symmetry with respect to the origin
• These are ODD functions
• Their graphs appear the same on both sides of the origin.
• Algebraically for every x in the domain of f , f(-x)=-f(x)
![Page 6: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/6.jpg)
Example a
When graphed, appears
EVEN
Algebraically:
f(-x)=4(-x)2-1
= 4x2-1
=f(x)
x
y
![Page 7: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/7.jpg)
Example bWhen graphed, appears
ODD
Algebraically:
3
2
3
2
5
5( )
x
x
x
xf x
x
y
3
2
( )( )
( ) 5
xf x
x
![Page 8: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/8.jpg)
Example cWhen graphed, appears
Neither
Algebraically:
f(-x) = (-x)3+2(-x)2
= -x3+2x2
≠ f(x) or –f(x)
x
y
![Page 9: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/9.jpg)
Example dWhen graphed, appears
ODD
Algebraically:
f(-x) = 2(-x)3-3(-x)
= -2x3+3x =-(2x3-3x)
=-f(x)
x
y
![Page 10: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/10.jpg)
Example eWhen graphed, appears
Neither
Algebraically:
f(-x) = -(-x)2+0.03(-x)+5
= -x2-0.03x+5 ≠ f(x) or –f(x)
x
y
![Page 11: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/11.jpg)
Example fWhen graphed, appears
Even
Algebraically:
x
y
2
2
( ) ( ) 2
2
( )
f x x
x
f x
![Page 12: Today in Pre-Calculus Go over homework Notes: Symmetry –Need a calculator Homework.](https://reader036.fdocuments.us/reader036/viewer/2022062322/5697c0021a28abf838cc2dae/html5/thumbnails/12.jpg)
Homework
• Wkst.
• Quiz: Thursday, September 18