Question #618a7

1 Answer
Jan 8, 2018

You can't

Explanation:

To graph this function starting with #1/x#, first we need to write it in the form:
#y=a+b/(x+c)#

Given:

#y=(2x+3)/(5x-1)#

#y=2/5times(x+3/2)/(x-1/5)#

#y=2/5times(x-1/5+1/5+3/2)/(x-1/5)#

#y=2/5times((x-1/5)/(x-1/5)+(17/10)/(x-1/5))#

#y=2/5times(1+(17/10)/(x-1/5))#

#y=2/5+(34/25)/(x-1/5)#

As you can see, the denominator can't be in the form of just #x#.

To graph the function starting with #f(x)=1/x#

graph{1/x [-5, 5, -5, 5]}

We do the following transformations:

1) Shift #1/5# to the right:
#f(x-1/5)=1/(x-1/5)#

graph{1/(x-1/5) [-5, 5, -5, 5]}

2) Stretch vertically by a factor of #34/25#:
#34/25timesf(x-1/5)=(34/25)/(x-1/5)#

graph{(34/25)/(x-1/5) [-5, 5, -5, 5]}

3) Shift #2/5# up to get the final graph:
#34/25timesf(x-1/5)+2/5=2/5+(34/25)/(x-1/5)#

graph{(34/25)/(x-1/5)+2/5 [-5, 5, -5, 5]}