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