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