The Desmos Graphing Calculator
The Desmos online calculator allows users to graph mathematical functions/equations and to manipulate
the graphs on a computer, tablet, or whiteboard. Users can enter functions directly, or use sliders to
change parameters (key values) in a function. The effects of the changes are seen in real time.
The Desmos calculator can display multiple graphs in different colors simultaneously, trace along graphs,
locate points of intersection, and more.
Desmos in On Core
The Desmos Screen:
The version of Desmos used in the On Core whiteboard lessons is shown below.
•
The left side of the screen is for entering, editing, and manipulating functions. Key function
families are pre-loaded. Details are listed at the end of this document.
•
Functions are graphed and updated in real time on the right side of the screen.
•
Control buttons are at the bottom of the screen.
•
o
Undo/redo buttons allow you to step back/forward as desired.
o
Start over resets the screen.
o
Zoom in/out buttons change the scales.
o
The settings menu allows you to customize the grid scale, choose radian or degree
measure, and more.
The keypad (not shown below) appears at the lower left when you begin entering a function.
It enables you to enter function types, variables, numbers, and mathematical symbols.
Graphing Functions
Function Families
For On Core, the Desmos calculator provides several function families, shown in the list at the left side of
the screen.
Each function family has a parent (basic) form of the function, which is graphed by default in light blue.
For instance, the parent quadratic function is
.
Desmos also includes a more general form of the function, with letters indicating parameters that can
. Its graph is shown in darker blue.
change. This form of the quadratic function is
Sliders, used to change the parameters, are shown below the more general form of the function.
Using Sliders
To change the value of a parameter, use the slider to the lower right of the equation showing the current
parameter value. Tap a point along the slider line to change the value. The dark blue graph immediately
updates to reflect the change in the parameter’s value.
Entering Functions
To enter a new function while within a function family, go to the bottom of the list and tap “Click to add
equation” as shown at left below. To enter a new function outside of a function family, tap “start over,”
then tap “Start Fresh!” at the top of the function list, as shown at right.
In either case, the keypad appears at the lower left of the screen.
Using the Keypad
Use the keypad to enter:
•
Numbers and basic operational symbols.
•
Inequality symbols.
•
Variables (all letters on the keypad are treated as variables except e).
•
The constants e and π.
•
Radicals and powers.
•
Special functions, including trigonometric, logarithmic, square root, cube root, and absolute
value functions.
•
Parentheses.
To edit functions, use the arrow keys at the lower left of the keypad to move the cursor and the
delete key
at upper right to delete characters.
Parentheses, Functions, and Exponents
When you press the left parentheses key on the keypad, a pair of parentheses appears in the
function. Any characters you enter are inserted inside the parentheses until you tap—or use the
arrow keys to reposition the cursor—outside the parentheses.
Parentheses also appear for trigonometric functions such as
, logarithmic functions such as
, and some other functions. The absolute value function
that behave the same way the parentheses do.
displays absolute value bars
Exponents, and roots such as
, behave similarly, although parentheses are not visible. (The
same is true for superscripts and subscripts entered via the keypad.)
Editing Functions
To edit a function, tap inside its box. Then use the Desmos keypad to update the function’s box.
Deleting a Function
To delete a function, tap the close button to the upper right of the function.
Investigating Graphs
Tracing Along a Graph/Finding an Intersection Point
To trace a graph, tap it. The coordinates of the selected point appear. Tap any other location on the graph
to see the coordinates of another point.
To find the intersection of two graphs, tap close to the intersection point. The cursor “jumps” to the
intersection point, which looks like a “bull’s-eye.” The coordinates of the point are displayed.
Trace Point
Intersection Point
Changingg the Color of
o a Graph
To changee the color off a graph, highhlight the function box. Thhen tap the “C
Color” drop-down menu.
Tap insidee the color wh
heel to choose a color for the
t graph.
Zooming
To zoom in, “double-taap” the point you want to zoom
z
in on orr use the buttoon at the bottoom of the screen.
Hiding/Sh
howing Grap
phs
To hide a graph, uncheeck the box too the left of thhe function. To
T show the grraph, check thhe box again.
Changiing the Setttings
To custom
mize graph setttings, tap thee settings buttton at the low
wer right of thee screen. Usee the menu to::
Restore Defaults:
D
T
These
buttons (1) bring the center of the graph back too the
orrigin, (2) reseet the axes scaales so units on
o both axes are
a equal
(eensuring that graphs are noot distorted), and
a (3) reset the
t domain
annd range so sccales on both axes go from
m –10 to 10.
Axes and
d Grid:
U
Uncheck
thesee boxes to hidde axis labels, grid lines, annd the
x-- and y-axess.
Domain and
a Range:
E
Enter
new max
ximum and minimum
m
valuues for the x- and
a y-axes.
Grid Typ
pe:
C
Choose
betweeen Cartesian (rectangular)
(
or polar (circcular)
cooordinates.
Angle Meeasure:
For trigonomettric functionss, you can usee radian or deggree
m
measure.
Axis Labels:
For trigonomettric and trigonnometric inveerse functionss, you can
e
axis in terms
t
of π.
chhoose to displlay units on either
Function Families for Desmos in On Core
Family
Linear
Exponential Growth
Parent Function
General Form
Exponential Decay
| |
|
Square Root
√
√
a, h, k
Cube Root
√
√
a, h, k
Logarithmic, base
log
log
log
log
a, h, k
a, h, k
a, h, k
Sine
Cosine
Tangent
sin
cos
tan
sin
cos
tan
a, b, h, k
a, b, h, k
a, b, h, k
Absolute Value
Quadratic
Simple Polynomial
(Even)
|
Parameters
m, b
b, a, h, k
(b > 1)
b, a, h, k
(0 < b < 1)
a, h, k
a, h, k
n, a, h, k
(n is an even positive
integer)
n, a, h, k
(n is an odd positive
integer)
a, h, k
Simple Polynomial
(Odd)
Simple Rational
Exponential, base e
Logarithmic, base 2