Cubic Function and Reciprocal Function (ALDO ANDIKA)
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Transcript of Cubic Function and Reciprocal Function (ALDO ANDIKA)
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 𝑥 = 𝑎𝑥3 + 𝑏𝑥2 +𝑐𝑥 + 𝑑 . 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 𝑓 is the set of all real numbers
• The y intercept of the graph of 𝑓 is given by 𝑓 0 = d
• The x intercepts are found by solving the equation => 𝑎𝑥3 + 𝑏𝑥2 +𝑐𝑥 + 𝑑 = 0
FOR EXAMPLE • Draw the graph of 𝑦 = 𝑥3 + 4 𝑎𝑛𝑑 𝑜𝑓 𝑦 = −𝑥3 − 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 = 𝑥3 + 4 -212 -62 -4 4 12 68 220
Y = −𝑥3 − 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 = 𝑎
𝑥, where 𝑎 is a real number and 𝑎 ≠ 0. the
function y = 𝑎
𝑥is defined for all real values of x , except when x = 0
• For example: The table displaying values of x and y for y = 6
𝑥is:
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 TO
THE GRAPH
TEST YOUR SKILL! (CANNOT OPEN BOOK)
• Question 1:
• 1. copy and complete the following table which gives values of y = 𝑥3 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 =𝑥3 - 5 for values of x between -3 and 3 inclusive
X -3 -2 -1 0 1 2 3
Y -32 -6 22