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Key Ideas
Key Ideas
The parameters in a function or equation correspond to geometrical features of a graph and can represent physical quantities in spatial dimensions.
Our spatial frame of reference affects the visible part of a function and by changing this “window” can show more or less of the function to best suit our needs.
Functions represent mappings that assign to each value of the independent variable (input) one and only one dependent variable (output).A function acts like a machine much like an effects pedal with an input and output. Various knobs are used to decide what sound (or graph) comes out
I understand how any function can be transformed using values for "a, b, c and d"
I can explain how functions can be dilated, translated and reflected.
Linear Models
Linear Models
Quadratic and Polynomial Models
Quadratic and Polynomial Models
Graphs of Quadratic functions
Graphs of Quadratic functions
https://www.youtube.com/watch?v=ygH-Y5YG5kE
To skip ahead:
1) For how to find the X-COORDINATE of the vertex point from a STANDARD FORM equation of a parabola (like y = -2x^2 + 4x + 1), skip to time 0:16.
2) For how to find the Y-COORDINATE of the vertex, skip to time 1:34.
3) For how to get the vertex point from VERTEX FORM instead [like y = 2(x - 1)^2 + 3], skip to 2:24.
4) For what to do if the signs are confusing (ex. if the equation has X PLUS A NUMBER instead of x minus, like in y = 2(x + 3)^2 + 4), skip to 3:34.
End-behaviour of polynomials
End-behaviour of polynomials
Transformations: It works for any Function
Transformations: It works for any Function
Transformations Theory
Transformations Theory
Suppose we want to change the equation of a function so that its graph moves 4 units to the right and 2 units down and it also gets stretched twice as tall? What numbers in the equation do we need to change and how does the graph depend on those numbers?
We can use the parameters of a function to change its shape and appearance. This the enables us to match the function to data we have gathered or a phenomenon we wish to study
Transforming graphs.pdfModelling with Exponential functions
Modelling with Exponential functions
Game Reserve online lessons
Game Reserve online lessons
You are a detective and have been called to the Quietplanes Game Reserve. A dead elephant has been discovered just inside the reserve and it looks as if it has been the victim of poachers. As soon as you arrive you have the crime scene secured and the temperature of the elephant’s body is taken. The body temperature is 27C. You make sure that the elephant is not moved as the crime scene is searched for clues. The body temperature is taken again an hour later and found to be 24C.
It is vital for your investigation that you determine the time when the crime took place if you are going to identify or eliminate key suspects in the investigation. You have studied IB Mathematics and the police chief has put you in charge of working out when this crime took place.
https://www.geogebra.org/material/show/id/UDfpcUU7
Exponential Growth
Exponential Growth
https://www.youtube.com/watch?v=63udRYh04sY
In this video, we know that a population is growing exponentially; we also know there were 200 bacteria 3 days ago and 1000 bacteria yesterday. How many bacteria will be present tomorrow?
https://www.youtube.com/watch?v=-3MI0ZX5WRc
An Exponential Growth Problem. In this video, I review some basics about exponential functions, and do two problems related to exponential growth.
Exponential Decay
Exponential Decay
https://www.youtube.com/watch?v=K8IaH3adKz8
Radioactive Decay and Exponential Growth. In this video, we have a radioactive substance that decays at a constant percent rate. We use an exponential function to describe the amount of material.
https://www.youtube.com/watch?v=T7ivdB2qQyo
Exponential Decay / Finding Half Life - In this video, I find the half life of a substance that is decreasing annually by 4%.
Modelling with Trigonometric Functions
Modelling with Trigonometric Functions
Modelling using Trigonometric functions w. tech
Modelling using Trigonometric functions w. tech
Modelling with Trig functions w/o tech
Modelling with Trig functions w/o tech
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