Interactivate Syntax Reference

Syntax for Entering Functions in Interactivate Activities

• Numerical values entered should be accurately calculated from 10 ^-8 to 10 ⁸. Numbers larger or smaller than these values produce unreliable results. You may use scientific notation for entering functions in the form: mantissa followed by an e followed by 10 raised to the desired power. For example 0.000032 would be input as 3.2e10^-5.
• Functions and their compositions can be typed as follows:

Function	Symbol	Examples	Meaning
addition	+	x+3	x plus three
subtraction	-	5-x	five minus x
multiplication	*	x*(x-2)	x times the quantity x minus two
division	/	3/x	three divided by x
power	^	x^3	x to the power of three
power	**	x**3	x to the power of three
π	pi	sin(pi*x)	sine of the quantity π times x
square root	sqrt(...)	sqrt(x)	square root of x
nth root*	x^(1/n)	x^(1/3)	cube root of x
absolute value	abs(...)	abs(3-x)	absolute value of the quantity three minus x
e to the power of x	exp(...)	exp(x)	e to the power of x
sine	sin(...)	sin(2x)	sine of the product 2 times x
cosine	cos(...)	cos(5-x)	cosine of the quantity five minus x
tangent	tan(...)	tan(x)	tangent of x
arcsine	asin(...)	asin(x)	returns a value between -π/2 and π/2
arccosine	acos(...)	acos(x)	returns a value between 0 and π
arctangent	atan(...)	atan(x)	returns a value between -π/2 and π/2
secant	sec(...)	sec(x)	returns the secant of x, that is, 1/cos(x) if cos(x) ≠ 0
cosecant	csc(...)	csc(x)	returns the cosecant of x, that is, 1/sin(x) if sin(x) ≠ 0
cotangent	cot(...)	cot(x)	returns the cotangent of x, that is, 1/tan(x) if tan(x) ≠ 0
hyperbolic sine	sinh(...)	sinh(x)	hyperbolic sine of x
hyperbolic cosine	cosh(...)	cosh(10/x)	hyperbolic cosine of the quantity ten divided by x
hyperbolic tangent	tanh(...)	tanh(x)	hyperbolic tangent of x
natural logarithm	ln(...)	ln(x)	natural logarithm of x
base 10 logarithm	log(...)	log(x+5)	base ten logarithm of the quantity x plus five
positive part of the operand	ppo(...)	ppo(x+2)	returns x+2 if x+2>0 and 0 if x+2<0
step	step(...)	step(x)	returns 0 if x ≤ 0 and 1 if x > 0
floor	floor(...)	floor(x)	returns x rounded down to the nearest integer
ceiling	ceil(...)	ceil(x)	returns x rounded up to the nearest integer
factorial	fac(...)	fac(x)	returns 0 if x < 0, 1 if 0 ≤ x < 1, and 1×2× . . . ×floor(x) if x ≥ 1
sawtooth	saw(...)	saw(x)	returns x - floor(x), that is, the fractional part of x.
derivative	diff(...)	diff(2x^2 + 3x - 5)	returns 4x + 3
Area under curve from 0 to x	integ(...)	integ(sin(x))	returns 1-cos(x)
sign	sign(...)	sign(x)	returns -1 if x < 0, 0 if x = 0, and 1 if x > 0
square wave	square(...)	square(x)	returns sign(sin(x))
round x to the nearest integer	round(...)	round(x)	returns floor(x + 0.5)

* When x is less than zero, the exponent must be written as a whole number or in fraction form, not a decimal. For instance, if you want to graph the fifth root of negative numbers, you must write x^(1/5), not x^(0.2).