Examples of expression for functions that may be entered.

sin(pi*x)-x^2

arctan(2*x-2)-2

exp(x^2-1)+ln(x)

__How to use the calculator__

1 - Press on the button "click here to start" to start the calculator (applet).

__Interactive Tutorial__

## 1 - x and y intercepts of graphs

Enter x^2-2*x-3 in the editing window (which means f(x) = x^2-2*x-3) of the graphing calculator. Determine (approximately) the x intercepts of the graphs (these are the points of intersection of the graph with the x axis). Determine the y intercept (this is the point of intersection of the graph with the y axis).

The x intercepts are found by solving x^2-2*x-3 = 0 and the y intercept is given by f(0). Solve the equation x^2-2*x-3 = 0 and find f(0) and compare to the x and y intercepts determined graphically.

## 2 - Even and odd functions

Enter x^2 + abs(x) in the editing window (which means f(x) = x^2 + abs(x) , abs means absolute value). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests for even: f(x) = f(-x) and for odd: f(x) = - f(-x).

Enter x^3+1/x in the editing window (which means f(x) = x^3+1/x). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests.

Enter x^3+abs(x) in the editing window (which means f(x) = x^3+abs(x)). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests

## 3 - Determine Domain of a Function From Graph

Enter sqrt(4 - x^2) in the editing window (which means f(x) = sqrt(4 - x^2) , sqrt means square root). Verify graphically that the domain of f is given by the interval [-2 , 2].

Enter sqrt(-x + 1) in the editing window (which means f(x) = sqrt(-x + 1). Use the graph of f to determine its domain.

Enter 1 / (x^2 - 1) in the editing window (which means f(x) = 1 / (x^2 - 1)). Use the graph of f to determine its domain.

As an exercise find the domains of the above functions and compare with the domains found graphically above.

If needed, Free graph paper is available.

More Graphing Calculators.