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Cubic Function and Reciprocal Function (ALDO ANDIKA)

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Robertus Aldo Andika

This document discusses graphs of cubic and reciprocal functions. It provides examples of cubic functions in the form f(x)=ax^3+bx^2+cx+d and describes their key properties: the domain is all real numbers, the range is all real numbers, the y-intercept is d, and the x-intercepts are found by solving the cubic equation. Graphs of the functions y=x^3+4 and y=-x^3-4 are shown as an example. The document also discusses reciprocal functions in the form y=a/x and provides a table of values for the function y=6/x as an example graph. Students are given practice questions to test their understanding of cubic functions

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GRAPHS OF CUBIC FUNCTION AND RECIPROCAL FUNCTION MATHEMATICS SUBJECT ALDO ANDIKA & JOSHUA PRANATA XI A SOCIAL JOHN PAUL’S SCHOOL 2013-2014
GRAPHS OF CUBIC FUNCTION ? It is a quadratic function that has the form f ? = ??3 + ??2 + ?? + ? . Where a, b, c, d are real numbers and A is not equal to 0 ? The domain of this function is the set of all real numbers ? The range of ? is the set of all real numbers ? The y intercept of the graph of ? is given by ? 0 = d ? The x intercepts are found by solving the equation => ??3 + ??2 + ?? + ? = 0
FOR EXAMPLE ? Draw the graph of ? = ?3 + 4 ??? ?? ? = ??3 ? 4 on the same axes, for values of x from -3 to 3 and use each graph to find a. The value of Y when x = 2 b. The value of x when y = 4 x -6 -4 -2 0 2 4 6 Y = ?3 + 4 -212 -62 -4 4 12 68 220 Y = ??3 ? 4 212 62 4 -4 -12 -68 -220
THIS IS THE RESULT FROM THE TABLE:
GRAPH OF RECIPROCAL FUNCTION ? The general form of a reciprocal function is y = ? ? , where ? is a real number and ? ≠ 0. the function y = ? ? is defined for all real values of x , except when x = 0 ? For example: The table displaying values of x and y for y = 6 ? is: X -15 -10 -5 -0,5 0,5 5 10 15 Y -0.4 -0,6 -1.2 -12 12 1.2 0.6 0.4
THIS IS THE RESULT FROM THE TABLE THE GRAPH
TEST YOUR SKILL! (CANNOT OPEN BOOK) ? Question 1: ? 1. copy and complete the following table which gives values of y = ?3 for values of x between -3 and 3 inclusive. X -3 -2 -1 0 1 2 3 y -8 1 27
TEST YOUR SKILL (CANNOT OPEN BOOK) ? Question 2: ? 2. Copy and complete the following table which gives values of y =?3 - 5 for values of x between -3 and 3 inclusive X -3 -2 -1 0 1 2 3 Y -32 -6 22

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Cubic Function and Reciprocal Function (ALDO ANDIKA)

  • 1. GRAPHS OF CUBIC FUNCTION AND RECIPROCAL FUNCTION MATHEMATICS SUBJECT ALDO ANDIKA & JOSHUA PRANATA XI A SOCIAL JOHN PAUL’S SCHOOL 2013-2014
  • 2. GRAPHS OF CUBIC FUNCTION ? It is a quadratic function that has the form f ? = ??3 + ??2 + ?? + ? . Where a, b, c, d are real numbers and A is not equal to 0 ? The domain of this function is the set of all real numbers ? The range of ? is the set of all real numbers ? The y intercept of the graph of ? is given by ? 0 = d ? The x intercepts are found by solving the equation => ??3 + ??2 + ?? + ? = 0
  • 3. FOR EXAMPLE ? Draw the graph of ? = ?3 + 4 ??? ?? ? = ??3 ? 4 on the same axes, for values of x from -3 to 3 and use each graph to find a. The value of Y when x = 2 b. The value of x when y = 4 x -6 -4 -2 0 2 4 6 Y = ?3 + 4 -212 -62 -4 4 12 68 220 Y = ??3 ? 4 212 62 4 -4 -12 -68 -220
  • 4. THIS IS THE RESULT FROM THE TABLE:
  • 5. GRAPH OF RECIPROCAL FUNCTION ? The general form of a reciprocal function is y = ? ? , where ? is a real number and ? ≠ 0. the function y = ? ? is defined for all real values of x , except when x = 0 ? For example: The table displaying values of x and y for y = 6 ? is: X -15 -10 -5 -0,5 0,5 5 10 15 Y -0.4 -0,6 -1.2 -12 12 1.2 0.6 0.4
  • 6. THIS IS THE RESULT FROM THE TABLE THE GRAPH
  • 7. TEST YOUR SKILL! (CANNOT OPEN BOOK) ? Question 1: ? 1. copy and complete the following table which gives values of y = ?3 for values of x between -3 and 3 inclusive. X -3 -2 -1 0 1 2 3 y -8 1 27
  • 8. TEST YOUR SKILL (CANNOT OPEN BOOK) ? Question 2: ? 2. Copy and complete the following table which gives values of y =?3 - 5 for values of x between -3 and 3 inclusive X -3 -2 -1 0 1 2 3 Y -32 -6 22