In this example, we illustrate the use of the TI-92 Graphing Calculator to construct a graph of a function. Graphing Calculators draw a graph by plotting many points. The table for these points is internal and we do not see it.

Example. Use a graphing calculator to graph f (x) = x² - 5x + 1 over [- 1, 6]. This is the same function used in the example above. When does the function decrease and when increase? What is the minimum value? When is it zero?

Solution: We use some of the first steps that were used in constructing a table of values.

The function is entered in the Graph mode:   1 

Display the Y= Editor:   and clear it:  8  

Enter the function in the entry line: x  2  5x  1 

At the top of the display screen is:  y1=x² - 5× x + 1

To display the WINDOW dialog box:  

We want to start at x = - 1: xmin=  1 

The interval we want is [- 1, 6], hence: xmax= 6 

Let the distance between the tick marks on X- axis be 1: xscl= 1 

We don’t really know what the range of y is so let’s use [- 10, 10]: ymin=  10 
ymax= 10 

Let the distance between the tick marks on Y- axis be 1: yscl= 1 

Let’s use the default value for xres= 2

F 1  (5 times to Labels)  2 

As we scan the graph from left to right (the positive x direction), note that the graph decreases to a minimum point then it increases. The minimum point within an interval may be found by using  and setting the lower and upper bounds for the interval. In the graph screen, pressing  will display the ‘Math’ menu. The minimum point is found as follows:

3 (minimum) displays a flashing cursor at the middle x value of the screen.

The zeros are found in a similar manner by placing bounds on the points where the curve intersects or touches the X-axis. The cursor may also be used in setting bounds.

Press  2 (zero)

When the cursor is to the left of the intersection, press  (this sets the lower bound). A pointer mark appears at the top.

Move cursor to the right of the intersection: press  (several times). When the cursor is to the right of the intersection, press 

The coordinates of this zero are xc: 0.208172 yc: 0.   The rightmost point of intersection of the graph and the X- axis is found in a similar manner.   Press  2 Hold down  press  several times until cursor is just left of this point, press    Move cursor to right of the point:      The coordinates of this zero are xc: 4.79129 yc: 0.

Problem. Use a graphing calculator to graph the function f (x) = - x² + 3x + 3 over [- 2, 5]. When does the function increase and when decrease? What is the maximum value? When is it zero?

Example. Use a graphing calculator to find the zeros of f (x) = 2x - 3.

Solution: The zeros are found using the home screen and the algebra menu ( ).

Display home screen and clear it:   8 Clear entry line: 

Display algebra menu and select ‘zeros’:  4

Enter the function, a comma, the variable, right parentheses: 2 x  3  x  

  for decimal form of answer which here is 1.5