Analysis & Approaches

Functions

Contents: Click to skip to subtopic

2.1

2.2

2.3/2.4

2.5

2.6

2.7

2.8

2.9

2.10

2.11

2.12

2.13

2.14

2.15

2.16

 

2.1: Linear functions

Problems:

  1. Find the slope of a line passing through (-1,0) & (3,-8):

  2. Parallel, perpendicular, or neither: y=3x+4 & y=3x+7

  3. Parallel, perpendicular, or neither: y+x/3=2 & y=3x-5

  4. Find eq. of a line that's parallel to y=0.5x+5 and passes (4,-5)

  5. Find eq. of a line that's perpendicular to y=2x-3 and passes (-5,3)

Answer
Answer
Answer
Answer
Answer
 

2.2: Domain, range, inverses

Problems:

  1. Find the range of f(x)=2ˣ + 1:

  2. Find the domain of g(x)=2x² - 3x + 2:

  3. If f(x)=0.2x - 6, find f¹(x):

  4. If g(x)=e²ˣ + 1, find g¹(x):

Answer
Answer
Answer
Answer
 

2.3/2.4: Graphs

 

2.5: Composite functions

Problems:

  1. If f(x)=2x & g(x)=3x+5, find (f º g)(x):

  2. If f(x)=2x & g(x)=3x+5, find (g º f)(x):

  3. If f(x)=x²+1 & g(x)=2x-7, find (f º g)(x):

  4. If f(x)=4/x, find (f º f)(x):

  5. If f(x)=4x²+x & g(x)=2x, find (f º g¹)(x):

Answer
Answer
Answer
Answer
Answer
 

2.6: Forms of quadratics

 

2.7: Solving quadratics

Video

Answer
Answer
Answer
Answer
Answer

Problems:

  1. Factor x² - 2x - 35:

  2. Factor 2x² + 5x - 3:

  3. Hence, find the roots of y = 2x² + 5x - 3:

  4. Solve 5x² - 27x + 10 = 0:

  5. 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]

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