Finding range of composite functions using GC
Suppose we want to sketch the curve C and the line y=-2x+2 on the same graph
Note how the line y-2x+2 is entered.
Adjust the Tmax to 1% more so the graph displays correctly.
Suppose we want to sketch the graph from -3 to 8.
2. Adjust the window setting to the required domain.
3. Trace the end point at -3 since it is not 1 complete cycle.
The following comparison are based on
TI 84 CE: Operating system 5.3.0
TI 84 Plus C: Operating system 4.2
Singapore Approved Operating System
New CONDITIONS submenu in “2nd test” allows faster entry of intervals for the piecewise functions
There are no major functional differences between TI 84 Plus CE and TI 84 Plus C. For piecewise functions, students should learn how to sketch manually without using the GC.
Enter the data in the GC as follows:
Variance can also calculated using the GC as follows:
Method 1: Change Xres to 3
The Xres button refers to pixel resolution (1 through 8). At Xres = 1, functions are evaluated and graphed at each pixel on the x-axis. At Xres = 8, functions are evaluated and graphed at every eighth pixel along the x-axis. Small Xres values improve graph resolution but may cause the calculator to draw graphs more slowly. Setting Xres to 3 provides good balance between speed and resolution.
Time taken to plot= 23.4 s
Time taken to plot= 3.6 s
Savings of almost 20 seconds! Which is crucial in exams
Method 2: Turn off “Detect Asymptotes”
The following example illustrates how we can use GC in Differential equations, and avoid the need to do integration to solve differential equation.
Solution for part ii
GC can be very helpful in solving certain problems in Complex Numbers.
Use the GC to find the real value of k such that has a complex root 1-i.
Since 1-i is a root,
Using TI 84 Plus (OS 2.55) to evaluate the complex numbers, we have
2+k = 0
Since the equation is quadratic, we can use the quadratic formula.
Using the GC to evaulate the above,
z = 1+2i or -7i
There are a total of 20 amusement rides in a theme park. A child insists on trying at least 5 of the amusement rides. Calculate the number of ways in which this can be done.
20 choose 5 + 20 choose 6 +… 20 choose 20
Using TI 84 OS (2.55)
sum (seq(20 nCr X, X, 5, 20, 1)
2^20- (20 choose 0+ 20 choose 1+20 choose 2+20 choose 3+ 20 choose 4)
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