Functions

Functions

ODDf(x) is odd if f(-x)=-f(x) turning points at x=a & x=-a rotational symmetry of order 2; 180° about origin Examplesy=sinxy=tanxy=3x^&-2x^5+3xy=1/x

EVENf(x) is even if f(-x)=f(x) turning points at x=a & x=-a reflective symmetry in the y-axis Examplesy=cosxy=x^2y=x^4y=3x^6-2x^4-5

PERIODICA periodic function repeats itself at regular intervals;y=sinx      Period = 2π or 360°y=cosx     Period = 2π/2 or 540°y=tanx     Period = π or 180°

CONTINUOUSThere are no breaks or gaps in the graph

MODULUS FUNCTIONS Sketch diagram For graphs under x-axis, change all signs Integrate each part seperately Add together the seperate signs

INVERSE FUNCTIONS Let y=f(x) Make x the subject Replace y by x to get required answer

More Functions

Let f(x) be monotonicIf f(x) is increasing ⇒ f(xmin) ≤ range ≤ f(xmax)If f(x) is decreasing ⇒ f(xmax) ≤ range ≤ f(xmin)

ROOTSA quadratic has real roots if b^2-4ac≥0

GRAPH SKETCHING Find any turning points, max & min* Find asymptotes - curve tending towards value Check behaviour of f near asymptotes Check behaviour of f as x→+∞

More Func 1 & 2 (image/png)

Vertical asymptotes Let denominator equation = 0 Factorise to get x-values NB: These CANNOT be touched or crossed!

More Func 3 Horiz (image/png)

More Func 4 Obliq (image/png)

Rubrica: : Horizontal Asymptotes

Rubrica: : Oblique Asymptotes