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Winter school revision bookletFunctions
1.1 Graphs – Grade 11 Summary and examples
The Parabola
2.1 Sketching a parabola
2.2 Determine the equation of a parabola
The Hyperbola
3.1 Sketching a hyperbola
3.2 Determine the equation of a hyperbola
The Exponential Graph
4.1 Sketching a exponential graph
4.2 Determine the equation of a exponential graph
Inverse Functions
Consolidation
6.1 Algebra
6.2 Functions
Grade 12 Tutoring Programme: MATHEMATICS 2
,1. GRAPHS – SUMMARY AND EXAMPLES
1.1 Summary of the GR11 Graphs
GRAPH NAME Parabola Hyperbola Exponential Graph
EQUATION 𝑦𝑦 = 𝑎𝑎𝑥𝑥 2 + 𝑏𝑏𝑏𝑏 + 𝑐𝑐 𝑘𝑘 𝑦𝑦 = 𝑎𝑎 𝑥𝑥+𝑝𝑝 + 𝑞𝑞
𝑦𝑦 = + 𝑞𝑞
𝑥𝑥 + 𝑝𝑝
WHAT YOU 𝑥𝑥 −intercepts 𝑥𝑥 −intercepts 𝑥𝑥 −intercepts
NEED to sketch
the graph. • 𝑦𝑦 = 0 𝑦𝑦 = 0 𝑦𝑦 = 0
𝑦𝑦 −intercepts 𝑦𝑦 −intercepts 𝑦𝑦 −intercepts
• 𝑥𝑥 = 0 𝑥𝑥 = 0 𝑥𝑥 = 0
TURNING POINT ASYMPTOTES ASYMPTOTE
Axes of Symmetry
𝑏𝑏
• 𝑥𝑥 = − • 𝑥𝑥 = −𝑝𝑝 • 𝑦𝑦 = 𝑞𝑞
2𝑎𝑎
• 𝑓𝑓 ′ (𝑥𝑥) = 0 • 𝑦𝑦 = 𝑞𝑞
EXAMPLE of the
SKETCH of the
graph
Grade 12 Tutoring Programme: MATHEMATICS 3
, 2. THE PARABOLA
2.1 Sketching a parabola
EXAMPLE 1:
Equations in the TURNING POINT form 𝒚𝒚 = (𝒙𝒙 + 𝒑𝒑)𝟐𝟐 + 𝒒𝒒
Given: 𝑓𝑓(𝑥𝑥) = (𝑥𝑥 + 1)2 − 4
1.1 Write down the turning point of 𝑓𝑓.
1.2 Determine the 𝑥𝑥-intercepts of f.
1.3 Determine the coordinates of the 𝑦𝑦-intercept of f.
1.4 Draw the graph of f. Clearly show the turning point and intercepts with the axes.
1.5 Use your graph to answer the following questions:
1.5.1 Give the range of 𝑓𝑓.
1.5.2 For which values of 𝑥𝑥 will
(a) 𝑓𝑓(𝑥𝑥) > 0
(b) 𝑓𝑓 ′ (𝑥𝑥) > 0
1.5.3 Determine the equation of ℎ where ℎ is the graph after 𝑓𝑓 moved 1 unit to
the right.
1.5.4 Write down the turning point for 𝑔𝑔 if 𝑔𝑔 is the reflection of 𝑓𝑓 in the 𝑥𝑥 −axis.
Grade 12 Tutoring Programme: MATHEMATICS 4
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