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Grade 12 Functions
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it provides you with explanations on the aspects of functions and the different graphs you get and how to draw them and has exercises for you to practice on extracted from past papers
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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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