# 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