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Relation or Function?

Function

The line does not cross the same x value twice.

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Function or Relation?

Relation

The line crosses the same value of x more than once.

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Cube Root

f(x)= ³√x

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What type of system?

Dependent System

m₁ = m₂ , b₁ = b₂

*Remember:

y = mx + b

(Slope-intercept form)

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What type of system?

Inconsistent

m₁ = m₂ , b₁ ≠ b₂

*Remember:

y = mx + b

(Slope-intercept form)

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What type of system?

Independent

m₁ ≠ m₂

*Remember:

y = mx + b

(Slope-intercept form)

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Identity

f(x) = x

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Square Root

f(x) = √x

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Square

f(x) = x²

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Cube

f(x) = x³

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Formula for a right triangle?

Pythagorean Theorem

a² + b² = c²

What is this?

y - y₁ = m(x - x₁)

Point Slope Form

Example:

m = 1/3 ; p = (-2,3)

y - 3 = 1/3 (x + 2)

*p = point on a graph

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Cube;   Square Root;   Square;   Identity;   Absolute;   or Cube Root?

Absolute

f(x) = |x|

-b±√0

2a

How many and what type of solutions?

-b±√-x

2a

How many and what type of solutions?

-b±√4 ^{<---Perfect Square}

                           2a

How many and what type of solutions?

Positive Perfect Square

2 rational solutions

-b±√7^{<-- Not a perfect square}

                                    2a

How many and what type of solutions?

Positive / Not a perfect square

2 irrational solutions

y = mx + b

What is this?

m₁ = m₂

Parallel or Perpendicular?

m_{1 *} m₂ = -1

Parallel or Perpendicular?

m₁ = - 1

           _m²

Parallel or Perpendicular?

(x - h)² + (y - k)² = r²

What is this?

Standard form for the equation for a circle.

Example:

(x - 1)² + (y +2)² = 9

The center is at (1, -2)

The radius is 3²

(x - h)² + (y - k)² = r²

Is (h,k) a point?

No.

(h,k) is the center of a circle and is not a point on the line.

(x - h)² + (y - k)² = r²

Is r² a point?

No.

 r² is the radius of the circle.

(x - h)² + (y - k)² = r²

How do you find a point for the graph of this equation?

1.) Use (h,k) to locate the center of the circle.

2.) Then move up, down, left, or right in the number of spaces away from that center as indicated by the radius.

3.) The point on the graph that you locate is a point on the line of the circle.

4.) By moving in the four cardinal directions from the center, you can mark each of those points and then draw the graph of the circle.

(x₁ + x₂ , y₁ + y₂)

2            2

What is this?

The Midpoint Formula

(x₁ , y₁) , (x₂ , y₂)

(x - h)² + (y - k)² = r²

Locate (h,k)

*Remember that

(x-h) = 0   (y-k) = 0

   x-h = 0     y-k = 0

     x = h         y = k

    d = √(x₂ - x₁)² + (y₂ - y₁)²

What is this?

The Distance Formula

(x₁ , y₁) and (x₂ , y₂)

(x₁ , y₁) and (x₂ , y₂)

How do you find the slope?

m = y₂-y₁

        x₂-x₁

i¹ = i

Divide 4 by the power of i.

Multiples of 4:

1 = i

2 = -1

3 = -i

4 = 1

Example:

(pg 109)

i⁵ = i⁴*i = i

i⁶ = i⁴*i² = -1

i⁷ = i⁴*i³ = -i

i⁸ = (i⁴)² = 1

i² = -1

Divide 4 by the power of i.

Multiples of 4:

1 = i

2 = -1

3 = -i

4 = 1

Example:

(pg 109)

i⁵ = i⁴*i = i

i⁶ = i⁴*i² = -1

i⁷ = i⁴*i³ = -i

i⁸ = (i⁴)² = 1

i³ = -i

Divide 4 by the power of i.

Multiples of 4:

1 = i

2 = -1

3 = -i

4 = 1

Example:

(pg 109)

i⁵ = i⁴*i = i

i⁶ = i⁴*i² = -1

i⁷ = i⁴*i³ = -i

i⁸ = (i⁴)² = 1

i⁸ = 1

Divide 4 by the power of i.

Multiples of 4:

1 = i

2 = -1

3 = -i

4 = 1

Example:

(pg 109)

i⁵ = i⁴*i = i

i⁶ = i⁴*i² = -1

i⁷ = i⁴*i³ = -i

i⁸ = (i⁴)² = 1

a + bi

Complex, irrational, imaginary?

Complex

Complex numbers are numbers that can be written in the form

a + bi

where a and b are real numbers and

i = √-1

p 106

√-x

Complex, irrational, imaginary?

Imaginary

i² = -1 and i = √-1

p 105

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Complex, irrational, imaginary?

Irrational

Someone had too much free time.

Also, pi is non-repeating and non-terminating.

As is pie.

p 3