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Cochino’s MathBy Jocelyn Hernandez, LeslieZamudio, Horacio Sevilla & YeseniaGonzalez
Functions and Their Graphs• Properties of Lines• Slope m=y2-y1/x2-x1,• Point slope y-y1=m(x-x1), Slope Intercepty=mx+b• Ve...
Basic Functions, Functions and Graphs• Function: A function has a value in the domain with exactlyone value in the range• ...
Transformations (Shifts, Stretches, andReflections)• Horizontal Translations:• Y=f(X-C) Translation to the right by C unit...
Transformations (Shifts, Stretches, andReflections)• Stretches and Shrinks:• Horizontal: Y=F(X/C) {A stretch by a factor o...
Combination of Functions• Sum: (F+G)=F(X)+G(X)• Difference: (F-G)(X)=F(X)-G(X)• Product: (FG)(X)=F(X)*G(X)• Quotient: (F/G...
Polynomials and Rational Functions• Ways to solve a Quadratic Equation: Factoring,Using the Quadratic Formula, Completing ...
Polynomials and Rational Functions• Synthetic Division:• Real zeros and complex numbers-complex numbers are numbers such a...
Polynomials and Rational Functions• Rational Functions :To graph a rationalfunction, you find the asymptotes and theinterc...
Polynomials and Rational Functions• Fundamental Theorem of Algebra• Any polynomial of degree n ... has n roots, butyou may...
Synthetic Division
Analytical Geometry• Parabolas•F(x)=x^2
Exponential and Logarithmic Functions• Exponential Function : f(x)=a.bx• Logarithmic Function:y= Logbx• Properties of Logs...
Exponential and Logarithmic Functions• Basic Common Logarithms Functions:• -Log101=0 because 100=1• -Log1010=1 because 101...
Ellipses with center(0,0)
Ellipses with center (h,k)
Hyperbolas
Hyperbolas center (0,0)
Hyperbolas center (h,k)
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Cochino’s math

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Transcript of "Cochino’s math"

  1. 1. Cochino’s MathBy Jocelyn Hernandez, LeslieZamudio, Horacio Sevilla & YeseniaGonzalez
  2. 2. Functions and Their Graphs• Properties of Lines• Slope m=y2-y1/x2-x1,• Point slope y-y1=m(x-x1), Slope Intercepty=mx+b• Vertical X=Y Horizontal Y=X
  3. 3. Basic Functions, Functions and Graphs• Function: A function has a value in the domain with exactlyone value in the range• Domain: The input or (x)• Range: The output or (y)• Vertical line test: if it passes it’s a function• Solving for a function: Algebraic, Numeric or Graphically• Continuity of a graph: Contiguous• Increasing and decreasing graphs.• Asymptotes: a line that a graph approaches but neverreaches
  4. 4. Transformations (Shifts, Stretches, andReflections)• Horizontal Translations:• Y=f(X-C) Translation to the right by C units• Y=f(X+C) Translation to the left by C units• Vertical Translations:• Y=F(X)+C Translation up by C units• Y=F(X)-C Translation down by C units• Reflections across the X-axis: y=-f(x)• Reflections across the Y-axis= f(-x)
  5. 5. Transformations (Shifts, Stretches, andReflections)• Stretches and Shrinks:• Horizontal: Y=F(X/C) {A stretch by a factor of Cif C>1}• {a shrink by a factor of C if C<1}• Vertical: Y=C*F(X) {A stretch by a factor of C ifC>1}• {A shrink by a factor of C if C<1}
  6. 6. Combination of Functions• Sum: (F+G)=F(X)+G(X)• Difference: (F-G)(X)=F(X)-G(X)• Product: (FG)(X)=F(X)*G(X)• Quotient: (F/G)(X)=F(X)/G(X), Provided G(X)cannot equal 0
  7. 7. Polynomials and Rational Functions• Ways to solve a Quadratic Equation: Factoring,Using the Quadratic Formula, Completing theSquare ax2 + bx = c• Polynomial Function• One-To-One Functions• Horizontal Line Test-If some horizontal line intersects the graph ofthe function more than once,then the function is notone-to-one.-If no horizontal line intersects the graph of thefunction more than once,then the function is one-to-one.
  8. 8. Polynomials and Rational Functions• Synthetic Division:• Real zeros and complex numbers-complex numbers are numbers such as :4+3i , 5i+i etc...• real zeros are the intercepts of a quadraticequation
  9. 9. Polynomials and Rational Functions• Rational Functions :To graph a rationalfunction, you find the asymptotes and theintercepts, plot a few points, and then sketchin the graph example equation:
  10. 10. Polynomials and Rational Functions• Fundamental Theorem of Algebra• Any polynomial of degree n ... has n roots, butyou may need to use complex numbers exampleof a polynomial• this one has 3 terms• The Degree of a Polynomial with one variable isthe largest exponent of that variable.
  11. 11. Synthetic Division
  12. 12. Analytical Geometry• Parabolas•F(x)=x^2
  13. 13. Exponential and Logarithmic Functions• Exponential Function : f(x)=a.bx• Logarithmic Function:y= Logbx• Properties of Logs:• Product: logbMN=logbM+logbN• Quotient: LogbMN=logbM-LogbN• Power: LogbNy=ylogbN
  14. 14. Exponential and Logarithmic Functions• Basic Common Logarithms Functions:• -Log101=0 because 100=1• -Log1010=1 because 101=10• -Log1010y=y because 10y=10y• -Loglogx=x because Logx=logx• Log always finds the exponent!!
  15. 15. Ellipses with center(0,0)
  16. 16. Ellipses with center (h,k)
  17. 17. Hyperbolas
  18. 18. Hyperbolas center (0,0)
  19. 19. Hyperbolas center (h,k)
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