# 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

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

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:

lilian-0716 | Student | (Level 1) Salutatorian

Posted on

a= positive or negative values

b= positive or negative values

c= positive, negative values or zero

so should we do different values?