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- https://math.libretexts.org/Courses/Coastline_College/Math_C170%3A_Precalculus_(Tran)/01%3A_Functions/1.03%3A_Domain_and_RangeIn creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.
- https://math.libretexts.org/Courses/Hartnell_College/MATH_25%3A_PreCalculus_(Abramson_OpenStax)/01%3A_Functions/1.02%3A_Domain_and_RangeIn creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.
- https://math.libretexts.org/Courses/College_of_Southern_Nevada/Calculus_(Hutchinson)/01%3A_Functions_and_Graphs_(Precalculus_Review)/1.02%3A_Basic_Classes_of_FunctionsFigure \PageIndex9: (a) For c>0, the graph of y=f(x)+c is a vertical shift up c units of the graph of y=f(x). (b) For c>0, the graph of y=f(x)−c is a vertical shift down ...Figure \PageIndex9: (a) For c>0, the graph of y=f(x)+c is a vertical shift up c units of the graph of y=f(x). (b) For c>0, the graph of y=f(x)−c is a vertical shift down c units of the graph of y=f(x). For c>0, the graph of f(x+c) is a shift of the graph of f(x) to the left c units; the graph of f(x−c) is a shift of the graph of f(x) to the right c units.
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/01%3A_Functions/1.03%3A_Domain_and_RangeIn creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_221_Calculus_1/01%3A_Functions_and_Graphs/1.03%3A_Basic_Classes_of_FunctionsWe begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.
- https://math.libretexts.org/Courses/Highline_College/MATHP_141%3A_Corequisite_Precalculus/03%3A_Inequalities_and_Functions/3.03%3A_Functions_and_Function_NotationThe set of the first components of the ordered pairs is called the domain and the set of the second components of the ordered pairs is called the range. \[\begin{array}{ll} h \text{ is } f \text{ of }...The set of the first components of the ordered pairs is called the domain and the set of the second components of the ordered pairs is called the range. h is f of aWe name the function f; height is a function of age.h=f(a)We use parentheses to indicate the function input.f(a)We name the function f ; the expression is read as “ f of a.”
- https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/01%3A_Functions_and_Graphs/1.02%3A_Basic_Classes_of_FunctionsWe begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.
- https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/01%3A_Functions_and_Graphs/1.03%3A_Basic_Classes_of_FunctionsWe begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.
- https://math.libretexts.org/Courses/Reedley_College/Calculus_I_(Casteel)/01%3A_Functions_and_Graphs/1.02%3A_Basic_Classes_of_FunctionsWe begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define gene...We begin by reviewing the basic properties of linear and quadratic functions, and then generalize to include higher-degree polynomials. By combining root functions with polynomials, we can define general algebraic functions and distinguish them from the transcendental functions we examine later in this chapter. We finish the section with piecewise-defined functions and take a look at how to sketch the graph of a function that has been shifted, stretched, or reflected from its initial form.
- https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_hdagnew@ucdavis.edu/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2F1%3A_Functions_and_Graphs_(Review)/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2F1%3A_Functions_and_Graphs_(Review)%2F%2F1.2%3A_Basic_Classes_of_FunctionsFor c>0, the graph of f(x+c) is a shift of the graph of f(x) to the left c units; the graph of f(x−c) is a shift of the graph of f(x) to the right c units. For example, the...For c>0, the graph of f(x+c) is a shift of the graph of f(x) to the left c units; the graph of f(x−c) is a shift of the graph of f(x) to the right c units. For example, the graph of the function f(x)=3x2 is the graph of y=x2 stretched vertically by a factor of 3, whereas the graph of f(x)=x2/3 is the graph of y=x2 compressed vertically by a factor of 3 (Figure \PageIndex8).
- https://math.libretexts.org/Courses/Fresno_City_College/Math_3A%3A_College_Algebra_-_Fresno_City_College/02%3A_Functions/2.02%3A_Domain_and_RangeIn creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this se...In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. In this section, we will investigate methods for determining the domain and range of functions.