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Lecture 1

Department

MathematicsCourse Code

MATH 2AProfessor

Shuhao CaoLecture

1This

**preview**shows pages 1-2. to view the full**6 pages of the document.**Math 2A – Calculus – 44095

Week 0 – Lecture 1 – Functions

Functions

•

o This symbol represents the set of all real numbers

o Written as letter R with a line cutting through it vertically

•

o Means that x is in the set R (R is a real number)

o This new symbol denotes that x belongs to (or is in, or an element of) R

Intervals

• Open Interval

o (-3, 5) = this states that x is a value from -3 to 5;

• Closed Interval

o [-3, 5] = this states that x is a value from -3 to 5 including 3 and 5;

• Hybrids

o (-3, 5]

▪ Means that

o [-3, 5)

▪ Means that

• Joining Intervals

o

▪ This union symbol indicates a joining

▪ Such that or

Domain and Range

• Input → → Output

o With being the function

o Input referring to the domain

o Output referring to the range

• A function can be thought of as a processor

o (has both an input and an output)

• Domain

o Is typically given the notation

o Refers to the set of all sensible inputs for the function given

o Example:

▪

▪ In this example, the domain cannot be negative, as it would yield an

impossible answer

▪ So therefore,

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• The second section of the above indicates the set notation

for a collection of numbers

• Range

o Range

o The collection of possible outcomes

▪ Found by plugging in the domain to the function

▪ Means that of in which has to be within the domain given

o

Piecewise Function

•

•

• Domain is in two parts, and if it doesn’t fall into the first category, it falls into the

other

Symmetry

• Even functions are functions such that

o These are symmetric with respect to the y-axis

o

• Odd functions are functions such that

o These are symmetric with respect to the origin

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