mhf4up unit 1 terms

polynomial function

degree ‘n’ is a function whose equation can be written in the form:

f(x) = a_nxⁿ + a_n-1x^n-1+ a_n-2x^n-2

n is a whole number (ex: W = {0, 1, 2, 3})

x is a variable

coefficients a_n, a_n-1, etc. are real numbers (ex: N = {1, 2, 3,...})

leading coefficient (a_n)

L.C is attached to the highest power of the variable

constant (a₀)

no variable

degree (n)

The exponent of the highest power of x

even degree function

a polynomial function whose highest exponent is an even number

ex: f(x) = 2x⁴ + x³ - 8

odd degree function

a polynomial function whose highest exponent is an odd number

f(x) = x³ + 4x² - 1

end behaviour

the direction in which a function travels - expressed by stating the starting and ending quadrants

polynomial power function

a polynomial of the form f(x) = axⁿ (passes through 0,0)

n is a whole number

x is a variable

a is a real number

even symmetry

function is symmetric over the y axis (specific type of line symmetry)

odd symmetry

the function is symmetric about the origin (a type of point symmetry)

• can be thought of like a 180 degree rotation about (0,0)