# f(x)=a/(bx+c) 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...

f(x)=a/(bx+c)

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

Expert Answers
embizze | Certified Educator

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 4th quadrants

` `b: performs a horizontal compression/stretch (this effect 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:

embizze | Certified Educator

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 should try both negative and positive values 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.

lilian-0716 | Student

a= positive or negative values

b= positive or negative values

c= positive, negative values or zero

so should we do different values?

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