Topics
3. Polynomials
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AustraliaVIC
VCE 11 Methods 2023

3.06 Graphs of polynomials

Lesson
Worksheet
Questions

Interactive practice questions

Does the graphed function have an even or odd power?

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A Cartesian plane has its $x$x-axis and the $y$y-axis ranging from $-10$−10 to $10$10. It is marked and labeled with integers at major intervals of $2$2 units, and is marked at minor intervals of $1$1 unit. The graphed function is a linear function. The line moves upward from left to right. The line passes through $\left(0,0\right)$(0,0) and extends beyond the visible part of the graph.

Odd

A

Even

B
Easy
< 1 min

Does the graphed function have an even or odd power?

Easy
< 1 min

Does the graphed function have an even or odd power?

Easy
< 1 min

Does the graphed function have an even or odd power?

Easy
< 1 min
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Outcomes

U1.AoS1.2

qualitative interpretation of features of graphs of functions, including those of real data not explicitly represented by a rule, with approximate location of any intercepts, stationary points and points of inflection

U1.AoS1.3

graphs of power functions f(x) = x^n for n=-2, -1, 1/3, 1/2, 1,2,3,4 and transformations of these graphs to the form y=a(x+b)^n+c

U1.AoS1.11

sketch by hand graphs of power functions f(x) = x^n for n=-2, -1, 1/3, 1/2, 1,2,3,4 and simple transformations of these, and identify any vertical or horizontal asymptotes

U1.AoS1.4

graphs of polynomial functions of low degree, and interpretation of key features of these graphs.

U1.AoS1.6

the key features and properties of power and polynomial functions and their graphs, including any vertical or horizontal asymptotes

U1.AoS1.10

sketch by hand graphs of linear, quadratic and cubic polynomial functions, and quartic polynomial functions in factored form (approximate location of stationary points only for cubic and quartic functions), including cases where an x-axis intercept is a touch point or a stationary point of inflection

U1.AoS1.12

draw graphs of polynomial functions of low degree, simple power functions and simple relations that are not functions

U1.AoS2.6

the connection between the roots of a polynomial function, its factors and the horizontal axis intercepts of its graph, including the remainder, factor and rational root theorems

U1.AoS2.7

solution of polynomial equations of low degree, numerically, graphically and algebraically, including numerical approximation of roots of simple polynomial functions using the bisection method algorithm

U1.AoS2.17

use algebraic, graphical and numerical approaches, including the factor theorem and the bisection method algorithm, to determine and verify solutions to equations over a specified interval

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