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Parent Functions
Who uses this?
Oceanographers use transformations of parent functions to approximate data sets such as wave height versus wind speed.
Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families or functions. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.
Who uses this?
Oceanographers use transformations of parent functions to approximate data sets such as wave height versus wind speed.
Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families or functions. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.
Video on parent functions
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Quadratic Functions
Why Would you want to learn this?
You can use quadratic functions to model the heights of a football,baseball, or soccer ball.
When a soccer ball is kicked into the air, how long will the ball take to hit the ground? The height, h, in feet of the ball after t seconds can be modeled by the quadratic function h(t)= -16t²+32t. In this situation the value of the function represents the height of the soccer ball. When the ball hits the ground, the value of the function is zero.
Why Would you want to learn this?
You can use quadratic functions to model the heights of a football,baseball, or soccer ball.
When a soccer ball is kicked into the air, how long will the ball take to hit the ground? The height, h, in feet of the ball after t seconds can be modeled by the quadratic function h(t)= -16t²+32t. In this situation the value of the function represents the height of the soccer ball. When the ball hits the ground, the value of the function is zero.
Video on Quadratic Functions
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Polynomial Functions
Who uses this?
Doctors can use polynomials to model blood flow.
A monomial is a number or a product of numbers and variables with whole number exponents. A polynomial is a monomial or a sum or difference of monomials. Each monomial in a polynomial is a term. Because a monomial has only one term, it is the simplest type of polynomial.
Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.
Who uses this?
Doctors can use polynomials to model blood flow.
A monomial is a number or a product of numbers and variables with whole number exponents. A polynomial is a monomial or a sum or difference of monomials. Each monomial in a polynomial is a term. Because a monomial has only one term, it is the simplest type of polynomial.
Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.
Video on polynomial functions
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Exponential Functions
Who uses this?
Collectors can use exponential functions to model the value of rare musical instruments.
Moore's law, a rule used in the computer industry, states that the number of transistors per integrated circuit (the processing power) doubles every year. Beginning in the early days of integrated circuits, the growth in capacity may be approximated by this table below:
year: 1965 1966 1967 1968 1969 1970 1971
Transistors: 60 120 240 480 960 1920 3840
Formula for an Exponential Function:
f(x)= b^n , where b > 0, b ≠ 1
Who uses this?
Collectors can use exponential functions to model the value of rare musical instruments.
Moore's law, a rule used in the computer industry, states that the number of transistors per integrated circuit (the processing power) doubles every year. Beginning in the early days of integrated circuits, the growth in capacity may be approximated by this table below:
year: 1965 1966 1967 1968 1969 1970 1971
Transistors: 60 120 240 480 960 1920 3840
Formula for an Exponential Function:
f(x)= b^n , where b > 0, b ≠ 1
Video on exponential functions
![Picture](/uploads/2/0/9/4/20943542/1331458.jpg)
Rational Functions
Why learn this?
Rational Functions can be used to model the cost per person for group events, such as a band trip to a bowl game.
A Rational Function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x)= 1/x. Its graph is a hyperbola, which has to separate branches.
Why learn this?
Rational Functions can be used to model the cost per person for group events, such as a band trip to a bowl game.
A Rational Function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x)= 1/x. Its graph is a hyperbola, which has to separate branches.