Polynomial FUNction Creator
In this task you will be building a polynomial function using various properties and representing this
function graphically and algebraically. You will then apply your function model to scenarios involving
transformations and rates of change.
Instructions for using this doc: Embed photos of your work under each question. Upload
completed file as a pdf to the Assignment folder in Brightspace named, "Function
Creator."
Part A: Function Creation
G). Write all six or seven digits in the space below.
Each digit will correspond to a value (A-
8
0
0
0
4
3
No
number
A
B
C
D
E
F
G
1. Create a polynomial function, \(f(x)\) of degree 3 or higher with the following
characteristics:
"D" is an x-intercept with multiplicity 1 or 2
"F" is the y-intercept
1a. Express your function in factored form and sketch a graph of your function by han.
Include any supporting algebraic and graphical evidence of your thinking. Label all key
points.
1b. State these other characteristics of your function: All x-intercepts, degree, domain,
range, end behaviours, number of turning points. If it is not possible to determine any
of these, justify why.
1c. Your function has been vertically reflected and horizontally translated by "E" units. If E=0,
use another value from your student number. Discuss which properties of the original
function will change and how you know. Include a graph of the new transformed
function, \(g(x)\).
1d. Determine the average rate of change of \(f(x)\) on the interval \(xE [-A, F]\).
1e. Is the instantaneous rate of change of the function constant over the entire domain of
the function? Explain how you know using graphical or algebraic evidence.
1f. Determine the instantaneous rate of change of \(f(x)\) at \(x = C\).
