Reciprocal Functions

The task today was to look at a function f(x) and its reciprocal 1/f(x). We were looking for connections between the two.

The first thing I asked groups (visible random) to do was graph y = x and the reciprocal y = 1/x. When they were done I had them graph y = x^2 and the reciprocal y = 1/x^2.

Here is what it looks like.

Whiteboarding Review

Students were put in visible random groupings and worked on vertical non permanent surfaces. The goal was to review concepts that we had seen in the activities in the course to date.

The first question asked them to list all characteristics of this piecewise graph.

Marble Paint Rolls and the Graphing Calculator

Students were put in random groups of three and were required to practise marble rolls until they could create a function with opposite end behaviour ( a cubic) and a function with the same end behaviour ( a quartic). Once they mastered it they put paint on their marble and made two marble paint rolls. Once it dried they went over it with a marker. They look like this.

Camping with Ms. Frizzle

Here was the task.
Going to Camp

 

The senior class is planning a wellness summer camp for two weeks.  The bus fare costs $500 and the cost is $275 per person for the two weeks.

 

Generate an equation for the total cost for the trip if n people are attending.

 

If everyone is going to share the costs equally then generate an equation for the cost per person if n people are attending.

 

Now if 8 people that want to attend cannot (because they cannot afford it) and the rest of the group decides to pay for them by splitting the extra costs equally. Generate an equation for the cost per person.

 

Create a table and sketch the graph for the last scenario.

State all of the following characteristics for the function in the last scenario: X Intercepts

Roots Zeros, Y Intercept, Domain, Range, End Behaviour, Maximum / Minimum Point(s), Intervals of increase, Intervals of decrease, Intervals of concave up, Intervals of concave down, Inflection Point(s), Asymptotes

Here is the student work:



 

Here is the task:

Shape rolling                                 

Introduction to the activity:

In this activity you are going to investigate the rolling of a geometric shape.  You will cut out a shape and poke a hole in the shape.  With your pencil in the hole, “roll” the shape along a straight edge at the bottom of your chart paper.

Overwijkitis

Here was the task.

Sept 11, 2014 BREAKING NEWS: Overwijkitis Virus Loose at Glebe

Strange behaviour at Carleton University last week has been linked to a new virus, called Overwijkitis, being researched in university labs.  University officials are strongly advising that students remain in their homes and away from anyone who may be infected.  Those who have been infected can be distinguished from others by a distinct red mark on their hands.  Anyone with these red marks is infected.

Zombies infect one other person per day in order to stay alive.  It is expected that the virus will spread next to neighboring towns and cities.

Characteristics and Speed Dating

What is a function?

 

 

Characteristics of functions.