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Simple functions of one variable can be graphed in three ways:

  • Typing  and then the equation

    Image Removed

    Typing the equation

  • Typing  and then the equation

    • Mathinline
    body--uriencoded--x%5e2

  • Typing

    Mathinline
    bodyy=
    and then the equation
    Mathinline
    body--uriencoded--x%5e3

  • Typing

    Mathinline
    bodyf(x)=
    and then the equation
    Mathinline
    body--uriencoded--\frac%7Bx%5e2%7D%7B7%7D

    Image Added

Functions can be hidden from the graph by clicking the colored circle to the left of their equation.

Functions can be functions of other functions. For example:

...

  • Mathinline
    body--uriencoded-- f(x)=
    x^{2}}{\displaystyle
    x%5e%7B2%7D

  • Mathinline
    bodyg(x)=f(x+1)
    }

Functions can be graphed with x in terms of y: {\displaystyle x={\sqrt {1-y^{2}}}}

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Functions can be of multiple variables. For example, {\displaystyle

Mathinline
body--uriencoded--g(a,b)=
a^{2}+b} and {\displaystyle
a%5e%7B2%7D+b
and 
Mathinline
body h(a)=g(a,3)
}
.

Parametric Equations

In Desmos you can graph parametric equations. The standard form of this is {\displaystyle (f(t),g(t))}. For example, {\displaystyle (sin(2t),cos(3t))}. It is necessary to use the variable {\displaystyle t} in order for the equation to be interpreted as a parametric equation.

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Input

Result

Explanation

exp(x)

exp(x)

Image Removed

Mathinline
body--uriencoded--e%5ex

ln(x)

ln(x)

The natural log of x

log(x)

log(x)

The log (base 10) of x

log_n(x)

Image RemovedImage Added

The log (base n) of x

x^n

x to the nth power

sqrtx

Image Removed
Mathblock
\sqrt{x}

The square root of x

nthrootx

Image Removed
Mathblock
\sqrt[\leftroot{-3}\uproot{3}n]{x}

The generalized root function.

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Input

Result

Explanation

sum

Image Removed
Mathblock
\sum_{n=}

The summation operator

prod

Image Removed
Mathblock
alignmentcenter
\prod_{n=}

The product operator.

int

Image Removed

Mathblock
alignmentcenter
\int

The integral operator.

d/dx

Image Removed

Mathblock
alignmentcenter
\frac{d}{dx}

The differential operator. Can be used on functions.

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Function

Explanation

total()

Sum of all elements in a list

length()

Number of elements in a list

mean()

Mean of a list

median()

Median element in a list

min()

Minimum element in a list

max()

Maximum element in a list

quantile()

The quantile function

mad()

Mean absolute deviation

stdev()

Sample standard deviation

stdevp()

Population standard deviation

var()

Variance

cov()

Covariance

corr()

Pearson correlation coefficient of two lists

nCr()

Number of combinations

nPr()

Number of permutations

Mathinline
body!

Factorial

Miscellaneous Functions

Input

Explanation

lcm(a,b)

The least common multiple of a and b

gcd(a,b)

The greatest common denominator of a and b

mod(a, b)

The modulo function

ceil(x)

The closest integer above x

floor(x)

The closest integer below x

round(x)

The closest integer to x

sign(x)

The sign of x

abs(x)

The absolute value function

Image Removed

Mathinline
body\mid x \mid

The absolute value operator

a%b

a percent of b

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To do this, click the wrench in the top right corner (graph settings). After this, a window will appear. In this window, there are inequalities for {\displaystyle x} and {\displaystyle y} ({\displaystyle

Mathinline
bodyx
and 
Mathinline
bodyy
 (
Mathinline
bodya\leq x\leq b
} and {\displaystyle
 and
Mathinline
bodyc\leq y\leq d
}
) which can be edited to resize the viewport with the domain set by {\displaystyle x}by
Mathinline
bodyx
 and range set by {\displaystyle y}by
Mathinline
bodyy
.

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Changing line colors/styles

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