What is a function?
Precise denitions
Domain and Range
Relations and graphs
Expressions as inputs
Examples
Quiz Review
Functions describe how one quantity depends on another
A quantity is a number together with a unit of measurement, such as feet or secon
NAME_
Math 195 Exam 1 Fall 2015
1. Solve and express your answer in interval notation. JUSTIFY your answer by showing your work.:
x4 18x2 < 3x3.
2. Solve for t:
5 x 3t 2 y t 2 y
(11 pt.)
(5 pt.)
1
195 Ex 1 F 15
5x + 9> 4
3. Solve and express your answer i
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Models seeking analysis
Analyzing the graph of a quadratic polynomial
Analyzing the graph of a cubic polynomial
Getting basic information from the graph of a function
A function is a collection of number pairs (x, y ), where x is an input and y = f (x) is
Combining and composing functions
Combining functions: algebraic methods
Functions can be added, subtracted, multiplied, divided, and raised to a power, just
like numbers or algebra expressions. If f (x) = x2 and g (x) = x + 2, clearly
f (x) + g (x) = x2
Lines and their slopes
Lines and their slopes
Parallel and perpendicular lines
Equations of lines
Quiz Review
Guide to SRW Section 1.10: Straight lines and their graphs.
Language note: In this course, the word line means straight line. If P and Q are
two
Formulas, functions, and inverse functions
The Question Man
Graphs of inverse functions
Quiz Review
Formulas and functions, forward and backward.
The formula y = x2 shows how y depends on x. The function denition f (x) = x2
shows how y = f (x) depends on
Transforming equations and graphs
Transforming graphs of functions
Sample problems
Examples: Six function transformations
Transforming equations and their graphs
The graph of the equation x2 + y 2 = 4 is a circle with center (0, 0) and radius 2.
The graph
The coordinate plane
Equations and their graphs
Finding points on graphs
Circles
Symmetry
Quiz Review
Analytic Geometry: the co-ordinate plane
All of mathematics and science relies on analyzing the graphs of equations. To get
started, we need to review th
Calculus saves the deer by using a cubic (degree 3) polynomial
At high noon, a volcano erupts. A deer standing d meters from the volcano
immediately runs away (moving along a straight line) at a speed of v meters per
second. The volcano spews lava at a ra
Welcome
Algebraic Expressions
Simplied sums
Greatest common factor
Factoring
Exercises
Quiz Review
Welcome to Math 19500 Video Lessons
Prof. Stanley Ocken
Department of Mathematics
The City College of New York
Fall 2013
An important feature of the followi
Welcome
Classifying real numbers
Factoring
Fraction rules
Adding fractions; LCD
Intervals
Innite intervals
Absolute value
Exercises
Quiz review
Welcome to Math 19500 Video Lessons
Prof. Stanley Ocken
Department of Mathematics
The City College of New York
Welcome
Whole number powers
Rewriting Fractions
Radicals and fractional exponents
Simplifying radicals.
Exercises
Quiz Review
Welcome to Math 19500 Video Lessons
Prof. Stanley Ocken
Department of Mathematics
The City College of New York
Fall 2013
An impor
How precalculus can save the dolphins
At high noon, an oil tanker explosion releases an oil slick on the surface of the ocean.
A dolphin located d meters (m) from the tanker immediately swims away from the
tanker in a straight line at a speed of v meters