Analysis & Approaches

Functions

Contents: Click to skip to subtopic

 

2.1: Linear functions

pg1 A&A HL - Topic 2 - Functions Notes.j

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
      -2      
Answer
Parallel
Answer
Perpendicular
Answer
y = 0.5x - 7
Answer
y = 0.5x + 5.5
 

2.2: Domain, range, inverses

pg2 A&A HL - Topic 2 - Functions Notes.j

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
    f(x)>1     
Answer
All real no's
Answer
f¹(x) = 5x - 30 
Answer
g¹(x)= 0.5ln(x-1)
 

2.3/2.4: Graphs

pg3 A&A HL - Topic 2 - Functions Notes.j
pg4 A&A HL - Topic 2 - Functions Notes.j
 

2.5: Composite functions

pg5 A&A HL - Topic 2 - Functions Notes.j

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
      6x+10      
Answer
6x + 10
Answer
4x²-28x+50
Answer
     x     
Answer
  x²+0.5x  
 

2.6: Forms of quadratics

pg6 A&A HL - Topic 2 - Functions Notes.j
 

2.7: Solving quadratics

pg7 A&A HL - Topic 2 - Functions Notes.j
pg8 A&A HL - Topic 2 - Functions Notes.j

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:

  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 

pg9 A&A HL - Topic 2 - Functions Notes.j

Video

 

2.9: Exponential & logarithmic functions 

pg10 A&A HL - Topic 2 - Functions Notes.
 

2.10: Solving equations

pg11 A&A HL - Topic 2 - Functions Notes.

Video

 

2.11: Transformations

pg12 A&A HL - Topic 2 - Functions Notes.

Standard Level content

 

Additional Higher Level content

2.12: Polynomials [AHL]

pg13 A&A HL - Topic 2 - Functions Notes.
pg14 A&A HL - Topic 2 - Functions Notes.
pg15 A&A HL - Topic 2 - Functions Notes.
 

2.13: More rational functions [AHL]

pg16 A&A HL - Topic 2 - Functions Notes.
 

2.14: Odd & even functions, self-inverse [AHL]

pg17 A&A HL - Topic 2 - Functions Notes.
 

2.15: Solving inequalities [AHL]

pg18 A&A HL - Topic 2 - Functions Notes.
 

2.16: Absolute value graphs, and more [AHL]

pg19 A&A HL - Topic 2 - Functions Notes.
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