Inverse Functions

Definition The inverse is shown by putting a little “-1” after the function name, like this: f-1(y), where y = f(x) It says “f inverse of y“ Here we have the function f(x) = 3x+2 The flow is Inverse Functions make 3x + 2 back to x , substitute y = 3x + 2, then So,

Lines of Symmetry of Plane Shapes

The line of symmetry is the axis or imaginary line that passes through the center of the shape or object and divides it into identical halves. How to find a shape has a Line of Symmetry ? You can find a shape has a Line of Symmetry or not by folding it When the folded

Asymptote: Definition, Horizontal, Vertical, Oblique, & Examples

Definition of Asymptote Asymptote is a line or curve that approach to another curve. It can be horizontal, vertical, or oblique asymptote. Asymptote is always approach to the curve but the distance is never zero. In another words, asymptote is never same as the curve. In mathematics, especially in analytic geometry, there are so many

Stem and Leaf Plots

Definition A Stem and Leaf Plot is a special table where each data value is split into a “stem” (the first digit or digits) and a “leaf” (usually the last digit). See this example: Example “47” is split into “4” (stem) and “7” (leaf). 10, 11, 22, 23, 24, 35, 36, 47, 48, 49 Stem

Function Transformations

How move and resize the graphs of functions? How move the graphs of functions? Add a constant to the y-value will move it up or down Add a constant to the x-value will move it left or right Examples Function c > 0 c < 0 f(x) = x2 g(x) = x2 + c        f(x)

Absolute Value

Definition of Absolute Value Absolute value or modulus |x| of a real number x is the non-negative value of x without regard to its sign. |x| = x for a positive x, |x| = −x for a negative x (in which case −x is positive) |0| = 0. For example, the absolute value of 5 is


Definitions Conjugate is where we change the sign in the middle of two terms The conjugate of “a + b” is “a – b” Conjugate is only used in expressions with two terms (binomials) Examples Expressions Conjugate a + 1 a – 1 b2 – 2 b2 + 2 4 + √3 4 – √3 When we

Pyramid: Definitions, Types, Surface Area, Volume, and Examples

Definition of Pyramid Pyramid is one of polyhedron form that connecting polygonal as the base and a point that called apex/vertex. As consequences there are base (polygonal that is like triangle, square, etc.) and some triangle sides as lateral sides. Type of Pyramid Depends on the Base Number of triangle depends on what type polygonal

Improper Fractions

Definitions There are 3 types of fractions Fraction type Condition Examples Proper Fraction Numerator < Denominator Improper Fraction Numerator > Denominator Mix Fraction A whole number + proper fraction So, An Improper Fraction is a fraction that has a top number larger than (or equal to) the bottom number. Converting Improper Fractions to Mixed Fractions How

Rationalize the Denominator

Irrational Denominator Denominator: the bottom number of fraction Rational: Numbers such as 2, 3, 7 Irrational: Roots such as √2, √3, √7 Simplest form of number cannot have the irrational denominator. To be in simplest form, Rationalizing the Denominator! Rationalizing the Denominator is making the denominator rational How to Rationalizing the Denominator Rationalizing the Denominator