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Summary maths functions revision grade 12
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FUNCTIONSPART 1
(REVISION FROM GRADE 11
ALL 4 GRAPHS)
GRADE 12
PAST EXAM PAPERS
EMAILBY
ADDRESS: melulekishabalala@gmail.com
MR M. SHABALALA CELLPHONE NUMBER: 0733318802 Page 1
@NOMBUSO
, 1. STRAIGHT LINE (LINEAR)
A) FORM
M in g L
gradient/slope , is a y intercept
iM
n n
INFORMATION FROM GRADIENT
′ ㄲ (g) straight line will be increasing ( / )
ᆐ ㄲ ( ) straight line will be decreasing ( \ )
M ㄲ straight line will be horizontal ( )
Distance M �ᚘ th ᚘ
M ambriabm straight line will be vertical )
Distance M ᚘth tᚘᚘt
B) STEPS TO SKETCH OR DRAW
1) Shape if m g ( /) m (\)
2) – intercept , let M and - intercept , let n M and plot
3) Join the points.
C) DOMAIN AND RANGE
DOMAIN possible values of n
RANGE possible values of
D) DETERMINING EQUATION
1) Determine the gradient
2) Substitute gradient and another point to solve for L using
( M in g L ) where i is a gradient
BY MR M. SHABALALA @NOMBUSO Page 2
, 2. PARABOLA (QUADRATIC)
A) FORM
M n g tn g L (standard form)
M n g h g (turning point form)
e.g n⪜ M n g g
Turning point (-3 ; 1)
To write equation in turning point form we need to complete the square.
B) STEPS TO SKETCH OR DRAW
1) Shape if a g ( happy face) a ( sad face)
2) – intercept , let M and - intercept , let n M
3) Turning point (NEW)
t n mbriaLihr g n mbriaLihr
Let n M or n M
Substitute to the original equation.
Examples sketch. M n g ng and Mn ng
C) DOMAIN AND RANGE
DOMAIN possible values of n
RANGE possible values of
coordinate at TP if g
coordinate at TP if
D) INTERPRETE( EFFECT OF am h)
( affect shape if a g ( happy face) and a ( sad face) OR Size if is
bigger the graph gets narrow and if is smaller graph gets wider
( Shift graph up or down. gup and down
h ( NEW Shift graph left or right. gright and left)
(Will be done in questions) EXEMPLAR 2013 and
NB: MAXIMUM or MINIMUM – coordinate of turning point is responsible for this
If g graph will have a minimum and if graph will have maximum
n mbriaLihr g n mbriaLihr
nM EXAMPLE NOVEMBER 2013
t
AXIS OF SYMMETRY nM
E) DETERMINING EQUATION
1) Given Turning point g another point
Substitute turning point to M n g h⪜ g , substitute point to get
2) Given any two points
Substitute both points separates and solve simultaneous.
3) intercepts g point.
Substitute to M n a⪜n 萒⪜ and then substitute a point to get
BY MR M. SHABALALA @NOMBUSO Page 3
, 3. HYPERBOLA
A) FORM
M g
ngh
h is the opposite of an asymptote (horizontal shift)
is y asymptote
EXAMPLE
ngl
M write down the values of p and q and asymptotes
ng
B) STEPS TO SKETCH OR DRAW
1) Draw all asymptotes (values that will make function undefined)
2) Shape if a g ( 1st and 3rd quadrant) a ( 2nd and 4th )
2) – intercept , let M and - intercept , let n M
3) Asymptotes
C) INTERPRETE
EXAMPLE
l
n M
ng
1) ASYMPTOTES
Vertical asymptote M horizontal asymptote M
2) Axis of symmetry
M ng M n 耀 (with Negative gradient)
M ng Mng (with Positive gradient)
3) DOMAIN: h
RANGE : h
BY MR M. SHABALALA @NOMBUSO Page 4
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