Analysis & Approaches
Functions
Contents: Click to skip to subtopic
2.1
2.3/2.4
2.7
2.8
2.10
2.11
2.13
2.1: Linear functions
Problems:
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Find the slope of a line passing through (-1,0) & (3,-8):
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Parallel, perpendicular, or neither: y=3x+4 & y=3x+7
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Parallel, perpendicular, or neither: y+x/3=2 & y=3x-5
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Find eq. of a line that's parallel to y=0.5x+5 and passes (4,-5)
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Find eq. of a line that's perpendicular to y=2x-3 and passes (-5,3)
Answer
-2
Answer
Answer
Perpendicular
Answer
y = 0.5x - 7
Answer
y = 0.5x + 5.5
2.2: Domain, range, inverses
Problems:
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Find the range of f(x)=2ˣ + 1:
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Find the domain of g(x)=2x² - 3x + 2:
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If f(x)=0.2x - 6, find f⁻¹(x):
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If g(x)=e²ˣ + 1, find g⁻¹(x):
Answer
f(x)>1
Answer
All real no's
Answer
f⁻¹(x) = 5x - 30
Answer
g⁻¹(x)= 0.5ln(x-1)
2.3/2.4: Graphs
2.5: Composite functions
Problems:
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If f(x)=2x & g(x)=3x+5, find (f º g)(x):
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If f(x)=2x & g(x)=3x+5, find (g º f)(x):
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If f(x)=x²+1 & g(x)=2x-7, find (f º g)(x):
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If f(x)=4/x, find (f º f)(x):
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If f(x)=4x²+x & g(x)=2x, find (f º g⁻¹)(x):
Answer
6x+10
Answer
6x + 10
Answer
4x²-28x+50
Answer
x
Answer
x²+0.5x
2.6: Forms of quadratics
2.7: Solving quadratics
Video
Answer
(x-7)(x+5)
Answer
(x+3)(2x-1)
Answer
x = -3 & 0.5
Answer
x = 0.4 & 5
Answer
Disc. = -59. So none
Problems:
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Factor x² - 2x - 35:
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Factor 2x² + 5x - 3:
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Hence, find the roots of y = 2x² + 5x - 3:
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Solve 5x² - 27x + 10 = 0:
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How many real roots does y = 3x² + 5x + 7 have?
2.8: Reciprocal & rational functions
Video
2.9: Exponential & logarithmic functions
2.10: Solving equations
Video
2.11: Transformations
Standard Level content
Additional Higher Level content
2.12: Polynomials [AHL]
2.13: More rational functions [AHL]
2.14: Odd & even functions, self-inverse [AHL]
2.15: Solving inequalities [AHL]
2.16: Absolute value graphs, and more [AHL]
