HP Prime: The Basics of Graphing (Function App)
Over the last few days, I have seen requests for a tutorial
of how to graph functions. I myself
received a request to do one.
This tutorial assumes that are using the most updated
version of the HP Prime. Be aware there has not been an update on the
iOS version yet (last version is 9069 as of 5/1/2016).
7/27/2016 Update: Sadly, version 10077 has been pulled due to issues and HP decided to take it off out of caution. The latest firmware is back to 8151. :( Affected areas will be deleted. Apologizes for any inconvenience. (yes, this sucks)
We are going to work with the Function App. Let’s get started.
The Three Main App Keys
[Symb]: The Symb
screen is where you enter up to ten functions, which are defined F1 to F9, then
F0.
[Shift] [Symb]: You
can change the angle measure, number format, and complex number format to be
specific to the Function App. I usually
just leave all three set at System (to borrow from System settings from Home
Settings)
[Plot]: The Plot
screen is the graph screen. You may drag
the screen to view different parts of the graph.
[Shift] [Plot]: This
is where you set up the plot screen, where you set the screen’s horizontal
boundaries (X Rng), the screen’s vertical boundaries (Y Rng), the tick marks (X
Tick, Y Tick). Scrolling down to page 2,
you can turn on or off Axes, Labels, grid dots, and grid lines. You have other options such as cursor and
method options. With the 10077 firmware,
you can set the background if desired.
For this tutorial, I will have the background turned off.
[Num]: This will
display a numerical table. (X, F1, F2,…).
[Shift] [Num]: Set
table options
Plotting Functions
Entering Functions on the Symb Screen
(Defining the function F(1)=X^2+3*X-1 and plotting it)
1. Press the [Symb]
screen.
Note: If you want to
clear all the functions that are defined, press [Shift] [Esc] (Clear) and press
the soft key (OK) to the “Clear all expressions?” prompt.
2. Enter your function. The independent variable is the capital
X. Press [Enter] or the soft key (OK)
when you are done.
3. To plot the
function, press the [Plot] key.
Note: You can change a function’s color. To do so, select the color box to the left of
the function and press either [Enter] or the (Choose) soft key. You can then choose from any of the eight
pre-selected colors or a custom color (lower-right square on the color palette).
Setting Easy Graphing Plot Setups
On the Plot screen, you can select pre-programmed plot
setups: Autoscale (my favorite),
Decimal, Integer, or Trig.
For the screen shots below, cleared the functions then
defined F1(X) = SIN(X) + COS(X) and set the calculator to Radian mode.
You can see the
difference below (based on the example, results may vary depending on the
functions defined):
Steps:
1. Press the [View]
key.
2. Select the
desired zoom setup (options 3 – 6).
Using the Plot Setup Screen
You can also use the plot up screen to set up the
boundaries. To do this:
1. Press [Shift]
[Plot].
2. To set the
Horizontal edges, select the X Rng row.
The left box is the Xmin (x-minimum, left side) and the right box is
Xmax (x-maximum, right side).
3. To set the
Vertical edges, select the Y Rng row.
The left box is the Ymin (y-minimum, bottom side) and the right box is
Ymax (y-maximum, top side).
4. If desired, you
can set the tick marks of the grid. To
do this, change the X Tick and Y Tick.
5. If desired, you
can press the page down soft key to turn axes, grid dotes, grid lines, and
labels on or off. Turning labels on will
show the range values on the plot screen.
6. To see the
changes, press the [Plot] key.
Note: If you want to
reset the graph screen to default settings, press [Shift] [Esc] (Clear). The default settings are: Xmin = -15.9, Xmax = 15.9, Ymin = -10.9, Ymax
= 10.9, X Tick = 1, and Y Tick = 1.
Setting the plot window as the following: Xmin = 0, Xmax = 2*π ≈ 6.28318530718, Ymin =
-2, Ymax = 2.
Tracing the Function
When you first graph functions, tracing is turned on automatically. That is when you press the directional pad
left and right, you follow the function.
If there are two or more functions plotted, you can press up or down to
select which function you want to trace.
You can also turn off tracing to allow the cursor to roam
freely, press the soft key (Menu) to call the menu. Press the (Trace ) soft key to toggle the
trace settings. Note when the menu isn’t
showing, you are seeing the coordinates of the cursor.
*(Trace*): Trace with
the dot showing, trace is turned on. The
cursor follows functions. The cursor
shows the X and function values.
*(Trace ): Trace
without the dot showing, trace is turned off.
The cursor is in free roaming mode.
The cursor shows the X and Y values.
Center the Plot Screen to Where the Cursor is Located
1. Move the cursor
to wherever want to center the plot screen.
2. Press the (Menu)
soft key to bring up the menu. Press
the (Zoom) soft key.
3. Select Center on
Cursor. That is all there is to it.
Zoom Using a Box
Zoom using a box (F1(X) = 2*COS(X) – 1)
1. Plot the function
(use the [Plot] key)
2. Press the (Menu)
soft key to bring up the menu. Press the
(Zoom) soft key.
3. Select Box… You will be prompted to select on corner of
the box. Press (OK) or [Enter].
4. Then select the
opposite corner. You will see the area
of zoom by a shaded box. Once you are
satisfied, press (OK) or [Enter].
5. The plot screen
is adjusted to the box you selected.
Move the Cursor to a Specific Position
You can send the cursor to a specific position. This is a useful function if you need to go
to a specific place. All you have to do
is press the (Go To) soft key. You will
be prompted for an X coordinate.
If Trace is turned on, the cursor moves to the X coordinate
and the function value. If Trace is
turned off, you will be prompted for both the X and Y coordinates.
For information regarding Definition and Transformation,
please see my post on the HP Prime 10077:
http://edspi31415.blogspot.com/2016/04/hp-prime-firmware-update-firmware-10077.html
Let’s explore some basic functions that you can operate on
the Function app.
The Root of a Function
To find the root (zero of a function):
1. On the Plot
screen, have Trace turned on (see above).
Select your function.
2. Press the (Fcn)
soft menu and select Root.
3. The HP Prime
finds the root that is closest to the cursor automatically.
Integrals
To find the area under the curve (numerical integral):
1. On the Plot
screen, have Trace turned on and select your function.
2. Press the (Fcn)
soft menu and select Signed Area.
3. Enter the lower
limit. You can use the directional pad
or enter a specific X value.
4. Enter the upper
limit. You can use the directional pad
or enter a specific Y value. Any area
above the x-axis is shaded in green and area shaded below the y-axis is shaded
in red.
5. Press (OK) or
[Enter]. The area is calculated.
Derivative
1. On the Plot
screen, have Trace turned on (see above).
Select your function.
2. Press the (Fcn)
soft menu and select Slope.
3. The HP Prime displays
the slope (derivative) automatically.
You can trace the function to display the slope at other points.
Intersection of Two Functions (or a Function and an Axis)
1. On the Plot
screen, have Trace turned on (see above).
Select your (first) function, and place the cursor close to the
intersection as possible.
2. Press the (Fcn)
soft key and select Intersection. You will be prompted to select the second
function or an axis.
3. The intersection
should be displayed.
Note: Make sure that
the cursor is close to the intersection you want. Otherwise, the function may not return an
answer.
This covers some of the basics of the Function App. There is a lot more to explore of this
app.
Eddie
This blog is property of Edward Shore, 2016.
