So far in mathematics 12, we have completed Investigation 1 and questions 1, 2, 5 and 6 in the text. This investigation asks you to explore nmber patterns and to develop sequences. We can find the sequence of differences by subtracting adjacent terms and use this difference to identify linear or other types of functions.
Some patterns that you may have noticed include:
- the common difference of your sequence is equal to the slope when you graph the data (if the common difference is 6, your equation may look like tn=6n)
- the first sequence of difference resulted in a common difference (the difference between the terms were the same) –> this tells us it is a linear function
- if you find the common difference between each term, you can then just figure out what constant needs to be added each time to find your equation y=mx+b
Some of the terms that we reviewed included:
- independent variable: is “manipulated” and can cause change in something else (ex. increasing the hours you work will change the amount that you are paid) – graphed on the x axis
- dependent variable: is dependent on something; changes in relationship to something (ex. the wage you are paid changes/depends on the hours you work)- graphed on the y axis
- domain: refers to the possible x values for your function
- range: refers to the possible y values for your function
For homework, page 4-6 questions #8, 10, 13, 14 and 15 were assigned. The due date for this homework is in class tomorrow (Wednesday).