Functions
and their
Graphs Grade 11
CAPS
Mathematics
Series
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Grade-11-Mathematics-Functions-and-their-Graphs.pdf, Study notes of Mathematics
In this topic you will : Revise the seven basic functions. 1. Unit. •. Investigate the effect of parameters. Unit 2. •. Generate new gr.
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Functions
and their
Graphs
Grade 11
CAPS
Mathematics
Series
Outcomes for this Topic
In this topic you will :
Revise the seven basic functions.
Unit 1
Investigate the effect of parameters.
Unit 2
Generate new gr
U
aphs.
nit 3
Seven Basic Functions
- The parabola function defined by y x^2.
- The exponential function define d by y ax.
- The sine function defined b y y s ni x.
We revise the following basic functions:
- The straight line function defined by y x.
- The cosine function defined b y y c so x.
3. The hyperbolic function define
d by y.
x
7. The tangent function defined b y y t na x.
Plot these points on Cartesian Plane.
Utilize at least the following three ordered pairs:
1 0 1 1 0 1
x y
Function defined by y x
Draw best fit graph.
Domain
Range
Plot these points on Cartesian Plane and draw graph.
Utilize at least the following six ordered pairs:
1 Function defined by y x
Horizontal Asymptote:
Defined by y 0
Vertical Asymptote:
Defined by x 0
2 1 1 1 1 2 2 2 1 1 2 2 1 1 2 2
x
y
Domain (^) x : x (^0)
Range (^) y : y (^0)
Symmetry Lines: y x y x
Plot these points on Cartesian Plane and draw best fit graph.
Function defined by ; 0; 1
x y a a a
Horizontal Asymptote:
Defined by y 0
Select 2 and utilize at least the
following five ordered pairs:
a
2 1 0 1 2 (^1 1 1 2 ) 4 2
x y
2
x
y
Domain Range (^) 0;
Plot points and sketch y sin x
360 270 180 90 0 90 180 270 360 0 1 0 1 0 1 0 1 0
x y
Period is 360 Range 1;1
Domain ;
Amplitude is 1
Finding points on y cos x
Utilize CAST diagram and Unit Circle
Complete table:
x y
Finding points on y tan x
Utilize information in the following three diagrams:
Complete tables:
360 270 180 90 0 90 180 270 360 0 0 0 0 0 315 225 135 45 45 135 225 315 1 1 1 1 1 1 1 1
x y x y
Plot points and sketch y tan x
360 270 180 90 0 90 180 270 360 0 0 0 0 0 315 225 135 45 45 135 225 315 1 1 1 1 1 1 1 1
x y x y
- • • •
- •
- •
Period is 180
Domain x : x 90 k 180 ; k
Vertical Asymptotes Range where x 90 k 180 ; k
Tutorial 1 Problem 1: Suggested Solution
- Sketch 3 if (^) 2;2 y x x
2 1 0 1 2 9 3 1 1 1 3 9
x y
•
Horizontal Asymptote:
Defined by y 0
D 2;2
R 0;9
Tutorial 1 Problem 2: Suggested Solution
2. Sketch y sin x if x 0 ;360
x y
D 0 ;360
Tutorial 1 Problem 4: Suggested Solution
- Sketch y tan x if x 90 ;90
90 45 0 45 90 1 0 1
x y
- •
D 90 ;90
Investigate
Effect of
Parameters
Unit 2