G-Solve
G-Solve is a graphical solving tool which allows you to find key features on a graph, including:
- x-intercepts.
- y-intercepts.
- Maximum of minimum points (turning points).
- Global (function) maximum or minimums.
Other actions and commands are also possible beyond this list - these will be introduced later.
Worked Example 1:
The features of G-Solve will be illustrated using the function f: ℝ → ℝ, f(x) = x2 + 3x - 10:
Figure 1 - The features available in the G-Solve list.
x-intercepts
To find the x-intercepts use "Root" from the G-Solve list:
Figure 2 - The x-intercepts (y = -10) found using the y-intercept command in G-Solve.
Therefore, the coordinates of the y-intercept are (0,-10).
y-intercepts
To find the y-intercept(s) use "y-intersect" from the G-Solve list:
Figure 3 - The y-intercept (x = -5 and x = 2) found using the Root command in G-Solve.
Therefore, the coordinates of the y-intercept are (0,-10).
Turning points
To find the turning point use "Min" or "Max" options from the G-Solve list:
Figure 4 - The turning point found using Min/Max command in G-Solve.
Therefore, the coordinates of the turning point are (-1.5, 12.25).
Note: G-Solve is a numerical tool; therefore, all answers given are decimalised and will not necessarily be exact. To find exact answers you need to refer to the main program.
Worked Example 2:
Additional features of G-Solve will be illustrated using the function f: [-1,2] → ℝ, f(x) = x2:
Function minimum
To find the function (global) minimum use "fMin" from the G-Solve list:
Figure 5 - The function minimum found using the fMin command in G-Solve.
Therefore, the coordinates of the function minimum are (0,0).
Function maximum
To find the function (global) maximum use "fMax" from the G-Solve list:
Figure 6 - The function maximum found using the fMax command in G-Solve.
Therefore, the coordinates of the function maximum are (2,4).
Note: Using the function minimum and function maximum commands we can determine the range of a function. for the function f: [-1,2] → ℝ, f(x) = x2 the range is [0,4].