Math 1111 – College Algebra<br />Chapter 1 – Equations & Inequalities<br />Section 1.1 – Graphs & Graphing Utilities<br />
Objectives<br />(1) Plot points in a rectangular coordinate system<br />(2) Graph equations in the rectangular coordinate<...
Plotting Points<br />Plot points in a rectangular coordinate system.<br />Plot the points A(1, 4), B(3, -2), C(-3, 0), and...
Plotting Points-Practice<br />Plot the points A(-1, -5), B(1, 1), C(1, 0), D(0, -2), and E(-4, 3)<br />
Rectangular Coordinate System<br />Quadrants<br />(+,+)…<br />Intercepts :<br />
Viewing Window (or Rectangle) of the Graphing Calculator<br />Make sure you know how to graph using a graphing calculator!...
Graphs of Equations<br />Point Plotting Method using a Table<br />Examples:<br />y=x<br />y=x2<br />y=|x|<br />Practice<br...
Identifying x- and y-intercepts<br />y=x2 -2<br />Practice exercises:<br />P. 98 #43-46<br />Does a graph always have x- a...
Math 1111 – College Algebra<br />Chapter 1 – Equations & Inequalities<br />Section 1.2 – Linear and Rational Equations<br />
Section 1.2 - Objectives<br />(1) Solve linear equations in one variable.<br />(2) Solve linear equations containing fract...
Solving a Linear Equation<br />Ex: <br />4x+5=29<br /> 4(2x+1)=29+3(2x-5)<br />
Solving a Linear Equation involving Fractions<br />1.<br />
Solving a Rational Equation<br />1.<br />2.<br />Write the value of the variable that make the denominator zero. This is y...
Categorizing an Equation<br />Three types:<br />Identity<br />Conditional<br />Inconsistent<br />Examples<br />
ICA 1<br />
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1.1 and 1.2 slides revised

  1. 1. Math 1111 – College Algebra<br />Chapter 1 – Equations & Inequalities<br />Section 1.1 – Graphs & Graphing Utilities<br />
  2. 2. Objectives<br />(1) Plot points in a rectangular coordinate system<br />(2) Graph equations in the rectangular coordinate<br /> system (“by hand” & with a graphing calculator)<br />(3) Interpret information about a graphing utility’s<br /> viewing rectangle or table (find points using tools on your graphing calculator)<br />(4) Use a graph to determine intercepts<br />(5) Interpret information given by graphs<br />
  3. 3. Plotting Points<br />Plot points in a rectangular coordinate system.<br />Plot the points A(1, 4), B(3, -2), C(-3, 0), and D(0, 5)<br />
  4. 4. Plotting Points-Practice<br />Plot the points A(-1, -5), B(1, 1), C(1, 0), D(0, -2), and E(-4, 3)<br />
  5. 5. Rectangular Coordinate System<br />Quadrants<br />(+,+)…<br />Intercepts :<br />
  6. 6. Viewing Window (or Rectangle) of the Graphing Calculator<br />Make sure you know how to graph using a graphing calculator!!!<br />Be able to set different windows.<br /> Be able to find intercepts/zeros with your graphing calculator.<br />Ex: [-10, 10, 1] by [-10, 10, 1]<br />[-10, 10, 2 ] by [-6, 6, 2 ]<br />[-5, 10, 1] by [-5, 5, 1]<br />[-10, 20, 5] by [-30, 50, 10]<br />
  7. 7. Graphs of Equations<br />Point Plotting Method using a Table<br />Examples:<br />y=x<br />y=x2<br />y=|x|<br />Practice<br />y=2x +1<br />y=x2 -2<br />y=2|x|<br />
  8. 8. Identifying x- and y-intercepts<br />y=x2 -2<br />Practice exercises:<br />P. 98 #43-46<br />Does a graph always have x- and y-intercepts?<br />Can a graph have the same x-intercept and y-intercept?<br />
  9. 9. Math 1111 – College Algebra<br />Chapter 1 – Equations & Inequalities<br />Section 1.2 – Linear and Rational Equations<br />
  10. 10. Section 1.2 - Objectives<br />(1) Solve linear equations in one variable.<br />(2) Solve linear equations containing fractions.<br />(3) Solve rational equations with variables in the denominators.<br />(4) Recognize identities, conditional equations, and inconsistent equations.<br />
  11. 11. Solving a Linear Equation<br />Ex: <br />4x+5=29<br /> 4(2x+1)=29+3(2x-5)<br />
  12. 12. Solving a Linear Equation involving Fractions<br />1.<br />
  13. 13. Solving a Rational Equation<br />1.<br />2.<br />Write the value of the variable that make the denominator zero. This is your restriction<br />Keeping the restrictions in mind, solve the equation <br />
  14. 14. Categorizing an Equation<br />Three types:<br />Identity<br />Conditional<br />Inconsistent<br />Examples<br />
  15. 15. ICA 1<br />
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