## 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*x cosine cos(...) cos(5 - x) cosine of the quantity five minus x tangent tan(...) tan(x) tangent 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 &le 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).

** The "integ" routine is slow at this time. Use sparingly.

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