Characteristics of functions
what is Domain & Range?
Domain: a set of values that are allowed to be plugged into a function, (a restriction for the x value)
Range: A set of outputs a function achieves when it is applied to its whole set of outputs, (a restriction for the y value)
what is an exponential function?
exponential function is a relation of the form y = ax, with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
What is a discrete function?
A function that is defined only for a set of numbers that can be listed, such as the set of whole numbers or the set of integers.
what are the special angles?
The special angles are 30 degrees, 45 degrees and 60 degrees.
What is a relation?
a relation defines the relationship between sets of values of ordered pairs. The set of elements in the first set are called domain which is related to the set of the element in another set, which is called range.
What is function notation?
Function notation is a way to write functions. Functions have a dependent and independent variable, and when we use function notation the independent variable is commonly x, and the dependent variable is F(x).
what is a graph in a exponential function?
The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.
What are real numbers?
A real number, is a quantity that can be expressed as an infinite decimal expansion.Real numbers are used in measurements such as size and time.
What is the unit circle used for?
This circle serves as an essential tool used to solve angular sines, cosine, and tangents, ultimately the lengths of triangles.
What is the amplitude of a function?
The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine.
what is the quadratic function equation?
Quadratic function equation is, f(x) = ax2 + bx + c
what is a table of values?
A table of values is a set of ordered pairs usually resulting from substituting numbers into an equation also known as a relation.
what is a discrete function?
A discrete function is a function with distinct and separate values.
What are the ratios for Sine, Cosine and Tangent?
sin = o / h
cos = a / h
Tan= o/a
What is the intersection of a function?
The points of intersection of two functions, f(x) and g(x), are the (x,y) coordinate pairs for which the input, x, results in the same output value from both functions
what is graphical representation?
Graphical representation refers to the use of charts and graphs to visually display and analyze, numerical data, functions.
What is a rationale exponent?
Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root.
A continuous function is a function that can take on any number within a certain interval.
What are reciprocal identities?
In trigonometry, reciprocal identities are sometimes called inverse identities. Reciprocal identities are inverse sine, cosine, and tangent functions written as “arc” prefixes.
What are polynomial expressions?
In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication.
what is a polynomial function?
A polynomial function is a function that involves only non-negative integer powers or only positive integer exponents of a variable in an equation like the quadratic equation or cubic equation.
what are the first two laws in the exponent laws?
1. The first law states that to multiply two exponential functions with the same base, add the exponents.
2. The second law states that to divide two exponential functions with the same base, subtract the exponents.
what is a recursive sequence?
A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given. If you know the nth term of an arithmetic sequence and you know the common difference d, you can find the (n+1)th term using the recursive formula an+1=an+d.
what are Sinusoidal functions?
The term sinusoidal is used to describe a curve, referred to as a sine wave or a sinusoid, that exhibits smooth, periodic oscillation.
what is a sequence?
A sequence is a function whose domain is the set of natural numbers or a subset of the natural numbers.