Solving
for X
for X
x2-9=0
Sol Set =[3,-3]
What is the point slope form?(What does the formula look like)
y-y1=m(x-x1)
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
f(x)=x2+4x+5, [1,3]
Farc=8
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
X2-25=0
Sol Set=[5,-5]
What form is this equation referred to: y=mx+b
Slope Intercept Form
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
Function:x2+3x
Interval:[1,3]
Farc=7
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}
X2+8x=-5
Sol Set=[7]
Write an equation for the line in point slope for the given points:
(1,2) and (3,-2)
f(x)=-2x+4
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
Find the average rate of change of the function from x=1 to x=4,f(x)=-x2-6x+5
Farc=-9
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
X2+4x+1=0
Sol Set=[-2+23, -2- 23]
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
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
Find the average rate of change for a line that passes through the points (1,3) and (5,10)
Farc=7/4
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
X2+12x+32=0
Sol Set=[-4,-8]
Find the equation of the line passing through the point (3,-1)with a slope of 2.
f(x)= 2x-7
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
Find the average rate of change of f(x)=4x-7 between x=-3 and x=5
Farc=4
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