what does a,b,c do?
Where a,b,c are an element of Z
a and b are not equal to 0
what would be the results, conclusions, patterns and other generalisations which you find?
include diagrams, graphs, summary tables etc
The parent function is `y=1/x` :
For `y=a/(bx+c)` :
a: performs a vertical stretch/compression. If a<0 then the graph is in the 2nd and 4the "quadrants
` `b: performs a horizontal compression/stretch (this effec is hard to see.)
There is a horizontal translation of `c/b` units left/right.
There is a vertical asymptote at `x=-c/b` (the horizontal translation moved the vertical asymptote.)
There is a horizontal asymptote at y=0.
example: `y=2/(x+3)` ; take the graph of `y=1/x` , move it 3 units to the left and stretch it with a factor of 2:
`y=-2/(x+3)` ; same graph as above but reflect across the horizontal axis:
a= positive or negative values
b= positive or negative values
c= positive, negative values or zero
so should we do different values?
If I was assigned this problem, I would try a number of different values for a,b, and c. I would change one of them at a time and note how the graph is affected.
You are correct that you should try both negative and positive value for each. You would end up with maybe 15 tables/graphs and the summary of how the graphs are changed when the variable is changed.
I just provided an overview.