Positive and negative equations, Domains, Formulas for Algebra

-2 - 1 =

-3

-3 x (-3) =

9

3 x (-3) =

-9

4/0 =

Undefined

√25 =

5

√6 =

2.44948974278

√-6 =

Undefined

0/4 =

0

Range

The number of outputs in a function.

-√25 =

-5

√-25 =

Undefined

(-2)³

-8

-4(-2)

8

1/8 (2)³

1

5 - (-4) =

9

(-8) - (-4)

-4

Domain

The values for which the function is defined.

ARC formula

f(max 𝑥) - f(min 𝑥)/Max 𝑥 - Min 𝑥 = f(𝑥) - f(𝑥)/Max 𝑥 - Min 𝑥 = ARC

(-4) - (-8)

4

1/8 x 8

1

ARC of Zero

Min f(𝑥) = Max f(𝑥)

5w³ * 4w²

20w⁵

4w³ * 3w

12w²

a * a²

a³

B - A

A: Being subtracted

B: Subtracting

Subtracting A from B means...

Start with B and then subtract A (B - A)

Define "Average Rate of Change"

Refers to the average rate at which a function changes over a given interval.

polynomial standard form

terms ordered greatest degree to least degree.

degree

the greatest exponent of its variable

Coefficient

The number in front of the variable in a term

(-5)²

25

Positive Arc

[min f(𝑥) < max f(𝑥)]

Negative Arc

[mix f(𝑥) > max f(𝑥)]

Standard form of (𝑥 + a) (𝑥 + b)

𝑥² + (a + b) + ab

Binomial form of 𝑥² + (a + b) + ab

(𝑥 + a) (𝑥 + b)

Product Property

√ab = √a * √b = a√b

Quotient Property

√a/b = √a/√b = √a/b

What property is √a+b = √a + √b

That is not a valid property, √a+b ≠ √a + √b

You can simplify square roots when no radical has a perfect square factor.

True

You can simplify square roots when there is no radical sign in the denominator.

True

Radical

√

Which of these formulas is not true?

√a+b = √a + √b

Which of these is not a factor of √144

12

Principle square root

√a = b

Which of these is not a solution for an Equivalent Equation?

Add/subtract one expression to the other

Equivalent equation

Equivalent equations are equations that have exactly the same solution (or solutions).

3¹²/y⁻¹⁰ is the same as

3¹² × y¹⁰

2⁻⁴ × z⁻³ is the same as

1/2²⁰ × z¹⁵

If 4⁻³ = 1/4³ then

4⁻³ = 1/64

If 4^½ = √4 then

4^½ = 2

If 8^¹/₃ = ³√8 then

8^¹/₃ = 2

If ⁷√v³ = (v³)^¹/₇ then

⁷√v³ = v^³/₇

If ⁶√g⁵ = (g⁵)^¹/₆ then

⁶√g⁵ = g^⁵/₆

If 5^¾ = (5³)^¹/₄ then

5^¾ = ⁴√5³

(⁵√3²)⁵ is equal to...

3²

If 16^¼ = 2 then

2⁴ = 16

𝑥²⁻½ is equal to...

𝑥^³/₂

⁴√𝑥 is the same as...

𝑥^¼

What does this equate to?

x^¹/₃

If (x^⁴/₃)^¼ = x^¹/₃ is the same as...

⁴√x^⁴/₃ = ³√x

√x^¼ is the same as

(x^¼) ^½

√x/x^¹/₃ is the same as

√x^²/₃