Operations on Functions - Graphing Calculator
An online graphing calculator to carry out operations on
functions. Five operations are supported by this calculator: addition, subtraction, multiplication, division and composition.
. The calculator has two inputs: one for function f and a second one for function g. Algebraic as well as trigonometric/a>, inverse trigonometric, exponential , logarithmic and hyperbolic functions may be used as input function. Here is a comprehensive list of basic functions and operators that may be used.
How to Use The Operations on Functions Calculator
Enter formulas for functions f and g and press the button corresponding to the operation to be carried out on functions f and g and explore the graphs of the three functions: f (in blue), g (in green) and the graph of function due to the operation carried out on f and g (in red). Five operations are supported by this calculator. (see more details on each operation below). Use the small letter x for the variable in the expressions of functions f and g .
Interactive TutorialSome tutorials and activities are suggested here but the use of this graphing calculator to explore and gain deep understanding of operations on functions is unlimited and any suggestions are welcome.1 - Addition of two functions
2 - Subtraction of two functions
3 - Multiplication of two functions
4 - Division of two functions
5 - Composition of two functions
Exercises1 - Let f(x) = sqrt(1-x) and g(x) = x^2. Input functions f and g and press on the button "(f o g)(x)". Estimate the domain of (f o g) from graph? Determine the domain analytically and compare.2 - Let f(x) = 1 - x and g(x) = sqrt(x). Input functions f and g and press on the button "(f - g)(x)". Using the graph, what do you think is the domain of f - g? Explain analytically. 3 - Let f(x) = 1 and g(x) = sqrt(x). Input functions f and g and press on the button "(f / g)(x)". Using the graph, what do you think is the domain of f / g? Explain analytically. 4 - Let f(x) = sqrt(1-x^2) and g(x) = sqrt(4-x^2). Input functions f and g and press on the button "(f * g)(x)". Estimate the domain of (f o g) from graph? Determine the domain analytically and compare. Solutions to above exercises: 1 - Since the domain of g is the set of all real numbers, the domain of (f o g)(x) is all values of x such that 1 - g(x) >= 0 or 1 - x^2 >= 0. Solving the inequality we obtain the domain as the interval: [-1 , 1] 2 - The domain of f - g is the intersection of the domain of f which is the set of all real numbers and the domain of g which is the set [0 , + infinity). The intersection is given by the interval [0 , + infinity). 3 - The domain of f / g is the intersection of the domain of f which is the set of all real numbers and the domain of g which is the set [0 , + infinity) also excluding any values of x that make the denominator of (f/g)(x) equal to zero (division by zero is not allowed). The intersection is given by the interval [0 , + infinity), exclude x = 0 since g(0) = 0, the final domain is given by (0,+infinity). 4 - The domain of f is the set of values in [-1,1] and the domain of g is the set of values in [-2,2]. The intersection of the two sets is [-1,1] More References and LinksTutorial on Composition of Functions.Properties of Trigonometric Functions Inverse Trigonometric Functions Graphs of Hyperbolic Functions Logarithmic Functions Exponential Functions Graphing Calculators. |