#Domain and range of a graph how to

No matter what amount you pay, you won't get a cheeseburger from a soda machine. Hence, the domain represents the inputs we can have here, that is, quarters and one-dollar bills. The machine will not give you any flavor of the soda if pennies are input. You can use quarters and one-dollar bills to buy a soda. Domain and range are the main aspects of functions. Similarly, for functions, we input different numbers and we get new numbers as the result. When you put in a certain amount of money, you can select different types of sodas. List all basic functions that are odd.ģ - List all basic functions that are neither even nor odd.Functions in mathematics can be compared to the operations of a vending (soda) machine.

List all basic functions that are even.Ģ - An odd function f has its graph symmetric with respect to the origin of the system of axes and therefore satisfy the condistion f(-x) = - f(x). TUTORIAL (5) - Identify Even and Odd Basic Functionsġ - An even function f has its graph symmetric with respect to the y axis and therefore satisfy the condistion f(-x) = f(x). TUTORIAL (4) - Compare the rate of change of the Basic Functionsġ - Which of the functions g(x) = x 2 or l(x) = e x increases faster as x increases?Ģ - Which of the functions f(x) = x or m(x) = ln x increases faster as x increases? TUTORIAL (3) - Intervals of Increase and Decrease and any local minimum or maximum of the Basic Functionsġ - For each function, write the interval(s) where the function increases and the interval(s) where the function decreases and the coordinate of any local minimum or maximum. Write inequalities involving x, x 2, x 3, √(x) and 3 √(x) on the intervals 0 1? Why are the graphs reflection of each other on the line y = x?Ĥ - Compare the graphs of f(x) = x, g(x) = x 2, h(x) = x 3, j(x) = √(x) and k(x) = 3 √(x). Why are the graphs reflection of each other on the line y = x?ģ - Compare the graphs of h(x) = x 3 and k(x) = 3 &radic (x).

#Domain and range of a graph how to

Compare the two function and use the definition of the absolute value to explain how to graph i(x) = | x | from the graph of f(x) = x.Ģ - Compare the graphs of l(x) = e x and m(x) = ln (x). Do this activity for all functions.ġ - Select function f(x) = x and function i(x) = | x |. Do this activity for all functions.Ĥ - Range : Select a function, examine its graph and its equation. Find the domain of the function being explored.

Do this for all functions in the applet.ģ - Domain : Select a function, examine its graph and its equation. TUTORIAL (1) - Domain and Range of Basic Functionsġ - click on the button above 'plot' to start.Ģ - Select a function and examine its graph. natural logarithmic function m(x) = ln(x).The answers to the questions in the tutorials are also included. The properties to be explored are: graphs, domain, range, interval(s) of increase or decrease, minimum or maximum and which functions are even, odd or neither. Graph, Domain and Range of Common FunctionsĪ tutorial using an HTML 5 applet to explore the graphical and analytical properties of some of the most common functions used in mathematics.