GMTC 0104 Q1 FPF.pptx

Lesson 4 Domain and Range of Functions  Objective At the end of this lesson, the learner should be able to Identify a function as being a linear, quadratic, polynomial, rational, or radical; find the domain and range of different types of function; and find the domain and range of a func...

Lesson 4 Domain and Range of Functions  Objective At the end of this lesson, the learner should be able to Identify a function as being a linear, quadratic, polynomial, rational, or radical; find the domain and range of different types of function; and find the domain and range of a function represented by its graph.  Essential Questions When do we say that a function is linear, quadratic, polynomial, rational, or radical? How can you find the domain and range of a function?  Warm Up! At this point, you should have already learned how to sketch the graph of functions. With a partner, work on the following online activity on graphing functions and be ready to answer the guide questions that will follow. “Graph Match.” Transum. Retrieved 04 March 2019 from https://www.transum.org/software/GraphMatch/  Guide Questions What strategy/strategies did you use to easily match the graphs with their corresponding equations? How does the graph look like when there is no given independent variable? How about when there is no dependent variable? For most of the functions given, each value of has a corresponding value of. In what situation(s) do you think this case does not happen?  Learn about It! Domain of a function 1 the set of all values of the independent variable that have corresponding values of the dependent variable Example: Consider the function. The domain of is the set containing all the first coordinates.  Learn about It! Range of a function 2 the set of all values of that can be obtained from the possible values of Example: Consider the function. The range of is the set containing all the second coordinates.  Learn about It! Linear function 3 a function that has a degree of 1 and whose graph is a straight line; the domain and range of a linear function are both the set of real numbers Example: The functions and are linear functions.  Learn about It! Quadratic function 4 a function that has a degree of 2 and whose graph is a parabola; the domain of a quadratic function is the set of real numbers Example: The functions and are quadratic functions.  Learn about It! Polynomial function 5 a function involving nonnegative integer powers of the independent variable; the domain of a polynomial function is the set of real numbers; the range of a polynomial function whose degree is odd is the set of real numbers Example: The functions and are polynomial functions. Constant, linear, and quadratic functions are also polynomial functions.  Learn about It! Rational function 6 a function that can be expressed as a ratio of two polynomials; the domain of a rational function is the set of real numbers except the zeros of its denominator Example: The functions and are rational functions. The domain of is the set of real numbers except. The domain of is the set of real numbers except.  Learn about It! Radical function 7 a function that contains radical expressions; the domain of a radical function is the set of real numbers except those that make the radicand of radicals with even index negative Example: The functions and are radical functions. What do you think are the domain of and the domain of ?  Try It! Example 1: Find the domain and range of the function.  Try It! Example 1: Find the domain and range of the function. Answer: The function is a linear function. The domain and range of a linear function are both the set of the real numbers. Therefore, the domain of the function is and its range is also.  Try It! Example 2: Find the domain and range of.  Try It! Example 2: Find the domain and range of. Solution: For a square root function to be defined, the radicand must be nonnegative (i.e. greater than or equal to zero). Therefore, the domain of is and its range is since the principal square root a number is always nonnegative.  Let’s Practice! Individual Practice: 1. What is the domain and range of. 2. Find the domain and range of using its graph.  Let’s Practice! Group Practice: To be done by 2-5 groups A ball is thrown upward with an initial velocity of 32 ft/s from a height of 10 ft. The height at any given time is given by What is the domain and range of this function? Key Points Domain of a function 1 the set of all values of the independent variable that have corresponding values of the dependent variable Range of a function 2 the set of all values of that can be obtained from the possible values of Linear function 3 a function that has a degree of 1 and whose graph is a straight line; the domain and range of a linear function are both the set of real numbers Key Points Quadratic function 4 a function that has a degree of 2 and whose graph is a parabola; the domain of a quadratic function is the set of real numbers Polynomial function 5 a function involving nonnegative integer powers of the independent variable; the domain of a polynomial function is the set of real numbers; the range of a polynomial function whose degree is odd is the set of real numbers Rational function 6 a function that can be expressed as a ratio of two polynomials; the domain of a rational function is the set of real numbers except the zeros of its denominator Key Points Radical function 7 a function that contains radical expressions; the domain of a radical function is the set of real numbers except those that make the radicand of radicals with even index negative  Synthesis How do you find the domain and range of different types of function? What are the rules or restrictions? How can you apply the concepts of domain and range of functions in your daily life as a student? Will the domain and range of two functions change when the functions are added or multiplied?