04/19/23 Perkins
AP Calculus AB
Day 2Algebra (Prereq sections 1-3)
• In the Y= menu, make
• GRAPH• x-int: Find the graph’s
zeros.1. CALC menu: ZERO
2. Left Bound? (use cursor or enter a number)
3. Right Bound?
4. Guess (only matters if there is more than one zero)
• y-int: Evaluate the function at x = 0.1. CALC menu: VALUE
2. Enter the number zero
3 4y x x 1. Find the x and y intercepts of using your calculator.
31 4y x x
4
2
-2
-4
-5 5
f x = x3-4x
Calculator: graph and find intersection point(s)
1. Enter both equations into Y=
2. GRAPH3. In the CALC menu: choose
INTERSECT4. First curve? (use up/down
arrows to choose)5. Second curve?6. Guess? (close to desired
intersection)7. Repeat for multiple
intersections.
2. Solve the system of equations using your calculator.
2 3x y 1x y
21
2
3
1
y x
y x
3
2
1
-1
-2
-3
-2 2
h x = x-1
g x = x2-3
2 5
1 4m
3
5 3
55 4y x
3 135 5y x
5
3m
532 1y x 5 53 32y x 5 13 3y x
3. Find the equation of the line through the points (-1,2) and (4,5).
4. Find the equation of the line through (-1,2) that is perpendicular to problem 3.
Manipulating Functions25. ( ) 2 1 ( ) 1f x x x g x x
. Find ( )a f x h
. Find b f g x
. Find c g f x
22 1x h x h
2 22 2 2 1x xh h x h
( )f g x 1f x
221 1 1x x
2 2 1 2 2 1x x x 2x
( )g f x 2 2 1xg x
2 2 1 1x x 2 2x x
Even / Odd functions
( ) ( )f x f x
3. ( )a f x x x
Even Functions have symmetry about the y-axis.
Odd Functions have symmetry about the origin.
The test is the same for either one: replace x with (-x).
If the function is EVEN: If the function is ODD:( ) ( )f x f x
6. Classify as even, odd, or neither one:2. ( ) 1b g x x
3( )x x xf 2
( ) 1x xg 3x x 2 1x
3x x ODD
EVEN
Note: with your calculator you can simply graph and look for symmetry.
6
4
2
-2
-4
-6
-5 5
6
4
2
-2
-4
-6
-5 5
Graphing Basics
( )f x cshifts graph vertically (+ up, - down)
Compared to
( )f x cshifts graph horizontally (re-centers at 0)x c
6
4
2
-2
-4
-6
-5 5
( )f xflips graph vertically (across the x-axis)
( )f xflips graph horizontally (across the y-axis)
( )f x
Perkins
AP Calculus AB
Day 2Algebra (Prereq Sections 1-3)
4
2
-2
-4
-5 5
3 4y x x 1. Find the x and y intercepts of using your calculator.
2. Solve the system of equations using your calculator. 2 3x y 1x y
3
2
1
-1
-2
-3
-2 2
3. Find the equation of the line through the points (-1,2) and (4,5).
4. Find the equation of the line through (-1,2) that is perpendicular to problem 3.
Manipulating Functions25. ( ) 2 1 ( ) 1f x x x g x x
. Find ( )a f x h
. Find b f g x
. Find c g f x
Even / Odd functions
3. ( )a f x x x
Even Functions Odd Functions
If the function is EVEN: If the function is ODD:
6. Classify as even, odd, or neither one:2. ( ) 1b g x x
Graphing Basics
( )f x c
Compared to
( )f x c
( )f x
( )f x
( )f x
6
4
2
-2
-4
-6
-5 5