MATH1100 Study Guide - Midterm Guide: Wolfram Alpha, Piecewise, Inverse Function
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Boston College
MATH 1100 – Calculus I
Spring 2016
Exam 1: 2/17/2016
Exam Guide
OneClass
Chapter 1
Function- when you put in a real number and get out a real number
Domain- the set of all real numbers that can be put into a function
• Pay attention if it is specified
• If unspecified assume it is as large as possible
• Restrictions:
o Can’t divide by 0
o Can’t take even roots of negative numbers
Example:
()=
, 3 because the denominator cannot equal zero
:(,3)(3, )
()=32 + , 7, 2 because you cannot take a square root of a
negative number
Domain
: [-2,7]
Piece-wise function- a function defined in multiple parts
• Graphs of these functions are all on the same plot
Example:
()=||+ 4
+< 1
1
Even vs. Odd
• Even function: f(x)=f(-x)
o Symmetry across y-axis
• Odd function: -f(x)=f(-x)
o Symmetry around the origin
• A function can be neither odd nor even
• To find:
o Plug in “-x” and see what comes out
Example:
()= even ()=odd
OneClass
Functions you should be able to graph and manipulate:
• Polynomials (especially linear/quadratic)
• Power functions
• Rational and algebraic functions
o Anything with +, -, ×, ÷, ,
• Trigonometric functions
• Logarithmic functions
• Exponential functions
Example:
=log() = sin() =cos()
=tan() = =
= 2 = 3 =
Transformations:
• Vertical shifts: y=f(x) +c
• Horizontal shifts: y=f(x-c)
• Vertical stretches: y=c × f(x) for c>0
• Horizontal stretches: y=f(x/c) for c>0
• Vertical flip: y=-f(x)
• Horizontal flip: y=f(-x)
OneClass