- f(x) = x
^{2}+ 1 - g(x) = log(x + 1)
- h(x) = 2x
- f(x) =
- p(x) = |x + 1|
- q(x) = [2x], where [x] gives the greatest integer less than or equal to x

- f(x) = x
^{2}+ 1

Domain = All real numbers (x can take any value)

Range [1, ∞). Minimum value of x^{2}is 0. - g(x) = log (x + 1)

Domain = Log of a negative number is not defined so (x + 1) > 0 or x > -1

Domain ( -1, ∞)

Range = (-∞, +∞)

Note: Log is one of those beautiful functions that is defined from a restricted domain to all real numbers. Log 0 is also not defined. Log is defined only for positive numbers - h(x) = 2
^{x}Domain - All real numbers.

Range = (0, ∞)

The exponent function is the mirror image of the log function. - f(x) =

Domain = All real numbers except -1

Range = All real numbers except 0. - p(x) = |x + 1|

Domain = All real numbers

Range = [0, ∞) Modulus cannot be negative - q(x) = [2x], where [x] gives the greatest integer less than or equal to x

Domain = All real numbers

Range = All integers

The range is NOT the set of even numbers. [2x] can be odd. [2 * 0.6] = 1. It is very important to think fractions when you are substituting values.

- Onto Functions
- Unconventional Question
- Quadratic Expressions
- Compound functions
- Greatest Integer Function
- Domain and Range

- Percents Profits & Interests
- DI - Bar Graphs
- Geometry
- VA - Sentence Rearrangement
- Speed Time Races
- DI - Pie Charts
- Coordinate Geometry
- VA - Sentence Elimination
- Ratio Mixtures, Averages
- DI - Multiple Graphs
- Trigonometry
- VA - Sentence Correction
- Logarithms and Exponents
- DI - Word Problems
- Mensuration
- VA - Para Completion
- Pipes Cisterns
- DI - Line Graphs
- Permutation; Probability
- VA - Text Completion