Pre-Calculus MATC1X3
3 May
Other Graphs
Other graphs
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Hyperbola: 𝑦 =
𝑘
𝑥−𝑝
+𝑞
Circle: (𝑥 − 𝑎)2 +(𝑦 − 𝑏)2 = 𝑟 2
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Exponential function: 𝑦 = 𝑎 𝑥
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Logarithmic function: 𝑦 = log 𝑎 𝑥
Sketch graphs:
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𝑦=
▪
𝑦=
6
+
𝑥−1
2
25 − (𝑥 − 1)2 + 2
Sketch
1
3
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𝑦 = ( )𝑥
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𝑦 = log 𝜋 𝑥
Summary
GRAPH
STANDARD FORM(S)
Straight Line
𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0 (General form)
𝑦 = 𝑚𝑥 + 𝑐 (Gradient-intercept form)
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) (Gradient point form)
Parabola
𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 (Polynomial form)
𝑦 = 𝑎(𝑥 − 𝑝)2 +𝑞 (Vertex form)
𝑦 = 𝑎(𝑥 − 𝑟)(𝑥 − 𝑠) (x-intercept form)
Hyperbola
𝑦=
Circle
(𝑥 − 𝑎)2 +(𝑦 − 𝑏)2 = 𝑟 2
Exponential
𝑦 = 𝑎𝑥
Logarithmic
𝑦 = log 𝑎 𝑥
𝑘
𝑥−𝑝
+𝑞
What to do
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Sketch graphs:
• Identify type of graph
• Find intercepts with access
• Find special points, e.g. vertex, asymptotes and centre of circle
Find equation if information is given:
• Identify type of graph
• Write down appropriate standard form
• Fill in given information
• Solve all parameters
Questions