Analysis & Approaches

Functions

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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)

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 f⁻¹(x):

4. If g(x)=e²ˣ + 1, find g⁻¹(x):

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 g⁻¹)(x):

2.6: Forms of quadratics

2.7: Solving quadratics

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]