Math 106

Solving for X

100

x²-9=0

Sol Set =[3,-3]

200

X²-25=0

Sol Set=[5,-5]

300

X²+8x=-5

Sol Set=[7]

400

X²+4x+1=0

Sol Set=[-2+²3, -2- ²3]

500

X²+12x+32=0

Sol Set=[-4,-8]

Find the Equation

100

What is the point slope form?(What does the formula look like)

y-y₁=m(x-x₁)

200

What form is this equation referred to: y=mx+b

Slope Intercept Form

300

Write an equation for the line in point slope for the given points:

(1,2) and (3,-2)

f(x)=-2x+4

400

Write the so;op intercept equation for the line with a slope of -3, that passes through the point (-4,1)

f(x)=-3x-11

500

Find the equation of the line passing through the point (3,-1)with a slope of 2.

f(x)= 2x-7

Interpret the Graph

100

Graph 1

1. DF: [-2,2]  RF=[-3,3]

2. Increasing: (-2,-1) u (1,2) 

    Decreasing: (-1, 1)

3. Local max:3@x=1

    Local min:-3@x=1

    Absol max:3@x=-1

    Absol min:-3@x=1

200

Graph 2

1. DF: [-4,6] RF:[-4,6]

2. Increasing: (-4,-3)u(-1,1)u(4,6)

    Decreasing: (-3,-1)u(1,4)

3. Local max:6@x=-3, 1@x=1

    Local min:-3@x=-1, -4@x=4

    Absol max:6@x=-3

    Absol min:-4@x=4

300

Graph 3

1. DF:(-00,+00) or IR RF: (-00,+00) or IR

2. Increasing: (-00,-2)u (2,+00)

    Decreasing: (-2,2)

3. Local max: 16@x=-2

    Local min: -16@x=2

    No Absol max/min

400

When do we know there is no absolute max/min?

What do we look for when identifying local max/min?

Arrows meaning goes on forever 

U shape, bell shape, curve shape

500

Graph 4

1. DF: (-00,+00) or IR RF: (-00,+00) or IR

2. Increasing: (-00,-3)u(-2,-1)u(2,+00)

    Decreasing: (-3,-2)u(-1,2)

3. Local max:3@x=-1, -2@x=-3

    Local min—3@x=-2, -4@x=2

    No absol max/min

Average Rate of Change

100

f(x)=x²+4x+5, [1,3]

Farc=8

200

Function:x²+3x

Interval:[1,3]

Farc=7

300

Find the average rate of change of the function from x=1 to x=4,f(x)=-x²-6x+5

Farc=-9

400

Find the average rate of change for a line that passes through the points (1,3) and (5,10)

Farc=7/4

500

Find the average rate of change of f(x)=4x-7 between x=-3 and x=5

Farc=4

Linear Functions

100

f(x)=3x+2

1. Slope/y-int.

2. Is f increasing, decreasing or constant? How do you know?

3.What is the average rate of change of f on the interval [-3/7,14]?

4.Domain/ Range

1. m=3/1, y-int.=(0,2)

2. Since m>0, then f is increasing

3. Farc= 3/1

4. DF=IR  RF=IR

200

f(x)= 0x+4

1. Slope/y-int.

2. Is f increasing, decreasing or constant? How do you know?

3.What is the average rate of change of f on the interval [-2/18,6]?

4.Domain/ Range

1. m=0, y-int.=(0,4)

2. Since m=0, f is constant

3. Farc=0

4.DF=IR  RF={4}

300

F(x)=3/4x+6

1. Slope/y-int.

2. Is f increasing, decreasing or constant? How do you know?

3.What is the average rate of change of f on the interval [7,27]?

4.Domain/ Range

1. m=3/4, y-int=(0,6)

2. Since m=3/4>0, then f is increasing

3.Farc=3/4

4.DF= IR  RF=IR

400

g(x)= -2/3+1

1. Slope/y-int.

2. Is g increasing, decreasing or constant? How do you know?

3.What is the average rate of change of g on the interval [-3/7,14]?

4.Domain/ Range

1. m=-2/3, y-int.=(0,1)

2.since m=-2/3<0, then g is decreasing

3. Garc=-2/3

4. DF= IR  RF=IR

500

h(x)= -3/4x-2

1. Slope/y-int.

2. Is h increasing, decreasing or constant? How do you know?

3.What is the average rate of change of h on the interval [-5.2,8.7]?

4.Domain/ Range

1. m=-3/4, y-int.= (0,-2)

2. Since m=-3/4<0, the h is decreasing

3. Harc= -3/4

4. DF=IR  RF=IR