A tutorial using an HTML 5 applet to explore the graphical and analytical properties of some of the most common functions used in mathematics. 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 . The answers to the questions in the tutorials are also included.

## Functions to be Investigated- linear function f(x) = x
- squaring function g(x) = x
^{2}
- cubing function h(x) = x
^{3}
- absolute value function i(x) = |x|
- square root function j(x) = √(x)
- cube root function k(x) =
^{3}√(x)
- natural exponential function l(x) = e
^{x}
- natural logarithmic function m(x) = ln(x)
## Interactive Tutorial Using Applet
## TUTORIAL (1) - Domain and Range of Basic Functions1 - click on the button above "plot" to start.2 - Select a function and examine its graph. Write down its equation .(for example f(x) = x ^{3}). Do this for all functions in the applet.
3 - Domain : Select a function, examine its graph and its equation. Find the domain of the function being explored. Do this activity for all functions. 4 - Range : Select a function, examine its graph and its equation. Find its range. Do this activity for all functions.
## TUTORIAL (2) - Comparing Basic Functions1 - Select function f(x) = x and function i(x) = | x |. 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.2 - Compare the graphs of l(x) = e ^{ x} and m(x) = ln (x). Why are the graphs reflection of each other on the line y = x?
3 - Compare the graphs of h(x) = x ^{ 3} and k(x) = ^{3}&radic (x). Why are the graphs reflection of each other on the line y = x?
4 - Compare the graphs of f(x) = x, g(x) = x ^{ 2}, h(x) = x^{ 3}, j(x) = √(x) and k(x) = ^{3}√(x). Write inequalities involving x, x^{ 2}, x^{ 3}, √(x) and ^{3}√(x) on the intervals 0 < x < 1 and x > 1?
## TUTORIAL (3) - Intervals of Increase and Decrease and any local minimum or maximum of the Basic Functions1 - 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.
## TUTORIAL (4) - Compare the rate of change of the Basic Functions1 - Which of the functions g(x) = x^{2} or l(x) = e^{ x} increases faster as x increases?
2 - Which of the functions f(x) = x or m(x) = ln x increases faster as x increases?
## TUTORIAL (5) - Identify Even and Odd Basic Functions1 - An even function f has its graph symmetric with respect to the y axis and therefore satisfy the condistion f(-x) = f(x). List all basic functions that are even.2 - 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). List all basic functions that are odd. 3 - List all basic functions that are neither even nor odd. |