MATH1100 Study Guide - Midterm Guide: Wolfram Alpha, Piecewise, Inverse Function

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10 Feb 2016
Department
Course
Professor
Boston College
MATH 1100 – Calculus I
Spring 2016
Exam 1: 2/17/2016
Exam Guide
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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
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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)
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