Piecewise Functions Definition A function can be expressed as a graph. But, not all of function has a whole graph. Some function has some pieces of the graph. It is called as piecewise function. The pieces of a function depend on x value that input into the formula/function. In another words, it is possible that
Cube is a special case of a prism. There are many things in daily life that is cube. Some of them are Rubik, dice, ice cube, aquarium, etc. Definition of Cube Cube is one of three-dimensional object. It has six squares as the sides (faces) so that it is also called hexahedron. Consequently, it has
Mathematical induction describe as a domino cards or climbing a ladder. In domino cards, if the first card falls, then the second falls too and so does the third, fourth and finally all of cards fall. Climbing a ladder is like domino cards. If the first step is passed, then going to second step, third
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,
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
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
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
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)
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