- #COMPOSITION OF FUNCTIONS CALCULATOR F OF G HOW TO#
- #COMPOSITION OF FUNCTIONS CALCULATOR F OF G FREE#
Using the graph, what do you think is the domain of f / g? Explain analytically.Ĥ - 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)". Using the graph, what do you think is the domain of f - g? Explain analytically.ģ - Let f(x) = 1 and g(x) = sqrt(x).
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.Ģ - Let f(x) = 1 - x and g(x) = sqrt(x). Input functions f and g and press on the button "(f o g)(x)". Is the domain of (f o g) what is expected? Explain.ġ - Let f(x) = sqrt(1-x) and g(x) = x^2. Definition: The domain of (f o g) is the set of all values of x such that g(x) is defined and real and also f(g(x)) is defined and real.(f o g)(2) and f(g(2)) should be very close if not equal. Estimate g(2) from graph (black) and now estimate f(g(2)) from graph (blue). Estimate (f o g)(2) from the graph (red). Let f(x) = sqrt(x) and g(x) = x^2, input functions f and g and press on the button "(f o g)(x)".Is it the intersection of the domains of f and g? Why is (f/g)(x) undefined at x = 1? What is the domain of f / g? Do the same at x = 4 and some other points. Let f(x) = sqrt(x) and g(x) = x - 1, input functions f and g and press on the button "(f / g)(x)".Explore the graph (in red) of function f / g is it what is expected? What do you think is happening at x = 0 for the graph of f / g? Let f(x) = 1 and g(x) = x, input functions f and g and press on the button "(f / g)(x)".Is it the intersection of the domains of f and g? Do the same at x = -1 and some other points.
Let f(x) = sqrt(x + 2) and g(x) = x, input functions f and g and press on the button "(f * g)(x)".Explore the graph (in red) of function (f * g)(x) is it what is expected? Compare the zeros of f, g and f * g and explain. Let f(x) = x - 2 and g(x) = x, input functions f and g and press on the button "(f * g)(x)".Do the same at x = 3 and some other points. Let f(x) = sqrt(x-2) and g(x) = x, input functions f and g and press on the button "(f - g)(x)".Explore the graph (in red) of function (f - g)(x) is it what is expected?.Let f(x) = x + 1 and g(x) = x, input functions f and g and press on the button "(f - g)(x)".Explore the domain of f + g graphically.Explore the graph (in red) of function (f + g)(x) take some specific values of x if necessary at x = 1 for example.Let f(x) = sqrt(x) and g(x) = x, input functions f and g and press on the button "(f + g)(x)".Some 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. Hover the mousse cursor on the top right of the graph to have the option of downloading the graph as a png file, zooming in and out, shifting the graphs. Hover the mousse cursor over the graph to trace the coordinates. Use the small letter x for the variable in the expressions of functions f and g. (see more details on each operation below). Five operations are supported by this calculator.
#COMPOSITION OF FUNCTIONS CALCULATOR F OF G HOW TO#
How to Use The Operations on Functions CalculatorĮnter 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).
#COMPOSITION OF FUNCTIONS CALCULATOR F OF G FREE#
If needed, Free graph paper is available. Also the argument of a function must be writtwn between brackets. NOTE: The multiplication operator * must be used explicitly whenever there is multiplication. Here is a comprehensive list of basic functions and operators that may be used.Įxamples of formulas for functions f and g, that you may copy and paste to use as inputs, are shown below: Algebraic as well as trigonometric, inverse trigonometric, exponential, logarithmic and hyperbolic functions may be used as input function. The calculator has two inputs: one for function f and a second one for function g. Operations on Functions - Graphing CalculatorĪn online graphing calculator to carry outįive operations are supported by this calculator: addition, subtraction, multiplication, division and Operations on Functions - Graphing Calculator >
0 kommentar(er)
