robert-barr
Uploaded by
14 SLIDES
293 VUES
150LIKES

Comprehensive Review of Relations, Functions, and Linear Equations

DESCRIPTION

This review covers fundamental concepts in relations and intervals, including set-builder and interval notation. It delves into defining relations, domains, and ranges, as well as identifying functions through various representations. Linear functions are analyzed through general forms, slope calculations, and intercepts. The review also addresses linear equations, inequalities, and their graphical solutions. Basic functions and their symmetry properties are examined, alongside transformations, providing a holistic understanding of these key algebraic concepts.

1 / 14

Télécharger la présentation

Comprehensive Review of Relations, Functions, and Linear Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Unit 1 Review

  2. 1. Relations and Intervals • Set-Builder Notation: {x | x>2} • Interval Notation: (2, ∞) • Relation: a set of ordered pairs • Domain and Range: input and output Determine domains and ranges from graphs. • Function: one to one relation Independent variable, dependent variable, vertical line test

  3. Exercise • Which of the following representations may describe a function? A. A set of ordered pairs B. An equation C. A graph D. All of these

  4. 1. Linear Functions • General form: f(x) = ax + b • Zero of a function: f(x) = 0, x is the zero of the function • X-intercept: zero of a function • Y-intercept: value of y when x = 0 • Constant function: y = a • Domain, Range of a linear function

  5. 1. Linear Function • Slope: (y2-y1)/(x2-x1), rate of change • Geometric orientation based on slope • Slope of a vertical line: undefined • Slope-Intercept form: f(x) = mx+b • Point-slope form: y-y1 = m(x – x1) • Standard form: Ax + By = C, A ≠ 0

  6. 2. Linear Function • Two parallel lines: equal slopes • Perpendicular lines: m1×m2 = -1 • Linear Regression

  7. exercise • Skills test 1: #4 • Skills test 1: #8 • Skills test 1: # 10

  8. 3. Linear Equation and Inequalities • Addition and Multiplication Properties of Equality • Graphical approaches to solving linear equations: Intersection • X-intercept method: f(x) = g(x) , find the zero of F(x) = f(x)-g(x)

  9. 3. Linear Equation and Inequalities • Addition and multiplication properties of inequality • Graph approach: f(x) > g(x) • X-intercept method of solution of a linear inequality: F(x) >0, x such that F is above the x-axis • Three party Inequalities

  10. exercise • Exam review: # 6 • Exam review: # 8

  11. 4. Basic Function and Symmetry • Basic Functions and their domain & range ,get to know their corresponding graphs • Symmetry with respect to the y –axis: f(x) = f(-x), even function • Symmetry with respect to the x-axis: not a function, if (a,b) is on the graph, then (a, -b) is also on the graph • Symmetry with respect to the origin: f(x) = -f(-x), odd function

  12. exercise • Skills test 1: # 29 • Skills test 1: #30 • Exam review: #13 • Exam review: # 14

  13. 5. Transformations • Vertical and horizontal shift • Vertical and horizontal stretching and shrinking • Reflection • Basic rules: f(x) = cf(bx + a) + d order: b, a, c, d

  14. exercise • Exam review: #16 • Exam review: # 17

More Related