×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

by: CJ Wechsler

97

3

4

# MATH 117, Study Guide #1 Math 117

CJ Wechsler
USC

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

This is the study guide for the first midterm, which covers through section 2.7. This study guide is an overview of the main ideas of each section. Examples of each can be found in the notes upload...
COURSE
Introduction to Mathematics for Business and Economics
PROF.
Matthew Thomas Hogancamp
TYPE
Study Guide
PAGES
4
WORDS
CONCEPTS
Math, functions, graphing equations
KARMA
50 ?

## Popular in Math

This 4 page Study Guide was uploaded by CJ Wechsler on Sunday September 25, 2016. The Study Guide belongs to Math 117 at University of Southern California taught by Matthew Thomas Hogancamp in Fall 2016. Since its upload, it has received 97 views. For similar materials see Introduction to Mathematics for Business and Economics in Math at University of Southern California.

×

## Reviews for MATH 117, Study Guide #1

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/25/16
Study Guide #1 1.4: Quadratic Equations 2 ax + bx + c = 0 Zero Factor Property: If ab = 0, then a = 0 or b = 0 2 Square Root Property: If x = k, then x = √k or x = -√k Completing the Square: 1) If a ≠ 1, divide by a 2) Move constant to own side of equation 2 3) Add (b/2) 4) Factor 5) Use square root property and solve 2 Quadratic Formula: -b ± √b -4ac / 2a discriminant: the solution to b -4ac to reveal the amount of solutions to the equation - if discriminant < 0 è no solutions - if discriminant = 0 è one solution - if discriminant > 0 è two solutions 1.7 Inequalities Notation: - [ ] are inclusive - ( ) are exclusive General Strategy: 1) Solve corresponding equation 2) Draw dots on number line 3) Test points on each side to determine interval **If rational inequality, find all values of x for which a side of the inequality is undefined (denominator is 0). Remove values from number line and use to make intervals 4) Shade appropriately 1.8 Absolute Values definition: distance from given number to zero Equation / Inequality How to Solve |a| = b a = ±b |a| < b -b < a < b |a| > b a < -b or a > b |a| = |b| a = ±b ** b ≥ 0 2.1 Rectangular Coordinates & Graphs Distance Formula: √(x – 1 ) +2(y - y 1 2 2 Midpoint Formula: (x + 1 / 22, y + y1/ 2)2 x-intercept: where curve of equation hits x-axis (y = 0) y-intercept: where curve of equation hits y-axis (x = 0) Drawing Graphs: 1) Find intercepts 2) Find other solutions 3) Plot and connect the dots 2.2 Circles 2 2 2 Center-Radius Form: (x-h) + (y-k) = r center: (h , k) radius: r General Form: x + y + Dx + Ey + F = 0 Convert center-radius form to general: FOIL Convert general form to center-radius: Complete the Square 2.3 Functions function: rule for assigning elements of one set to another set - machine with inputs and outputs Vertical Line Test: graph is a function if each x-value has 0 or 1 y-value - vertical line hits curve no more than once Increasing Interval: when x < x1impli2s f(x ) < f(1 ) 2 - uphill Decreasing Interval: when when x < x i1plies2f(x ) > f(x )1 2 - downhill Constant Interval: when f(x ) =1f(x ) 2 - flat ** intervals are always open (parentheses) because a specific point cannot be increasing or decreasing 2.5 Linear Models Point-Slope Form: m = y – y / x 1 x 1 Slope-Intercept Form: y = mx + b - lines are parallel if they have the same slope - lines are perpendicular if their slopes are opposite reciprocals 2.6 Graphs of Basic Functions continuous: interval where graph is connected; can be drawn without lifting pen discontinuous: interval where graph is broken piecewise function: defined by different rules over different intervals of its domain 2 3 Squaring function: f(x) = x Cube Root function: f(x) = √x Cubing function: f(x) = x 3 Absolute Value Function: f(x) = |x| Square Root function: f(x) = √x 2.7 Graphing Techniques y = a • f(x) Stretches or shrinks graph of f(x) vertically - If a > 1, stretch by factor of a - If 0 < a < 1, shrink by factor of a - If a < 0, first reflect across x-axis y = f(a•x) Stretches or shrinks graph of f(x) horizontally - If a > 1, shrink by factor of a - If 0 < a < 1, stretch by factor of a - If a < 0, first reflect across y-axis y = f(x) + a Translate (shift) graph of f(x) vertically y = f(x+a) Translate (shift) graph of f(x) horizontally

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Allison Fischer University of Alabama

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over \$600 per month. I LOVE StudySoup!"

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com