IB Maths AI 2.3 Definitions

This page contains our IB Maths AI definitions for 2.3. By learning each one of these definitions, you will fully cover the content for IB Maths AI 'Introduction to modelling functions'.

All Topic 2 Sub-topics 2.1: Forms Of Lines 2.2: Introduction To Functions 2.3: Introduction To Modelling Functions 2.4: Modelling Applications (HL)2.5: Further functions (HL)2.6: Graph transformations (HL)2.7: Advanced modelling functions (HL)2.8: Logarithmic graphs

axis of symmetry

The vertical line through the vertex of a quadratic, with equation

x=-\frac{b}{2a}

for

f(x)=ax^{2}+bx+c

gradient

The coefficient

a

y=ax+b

, giving the predicted change in

y

when

x

increases by

1

horizontal asymptote

A horizontal line

y=c

that an exponential graph approaches as

x

increases or decreases, for models such as

f(x)=ka^{x}+c

f(x)=ke^{rx}+c

quadratic model

A function of the form

f(x)=ax^{2}+bx+c

with

a \neq 0

, whose graph is a parabola and is suitable when there is a turning point.

roots

Values of

w

that satisfy an equation of the form

w^n=z

; for

z=r\operatorname{cis}\theta

, the

n

th roots are

w_k=\sqrt[n]{r}\operatorname{cis}\left(\frac{\theta+2k\pi}{n}\right)

for

k=0,1,\dots,n-1

vertex

A point in a graph.

vertical asymptote

A vertical line that a graph approaches but never reaches; for inverse variation models with

n \lt 0

f(x)=ax^{n}

, the line

x=0

(the

y

-axis) is a vertical asymptote.

y-intercept

The point where a line crosses the $y$ -axis, found by setting $x=0$ in the equation of the line.

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