The graph below is a vertical andor horizontal shift of y1x

The graph below is a vertical and/or horizontal shift of y=1/x (assume no reflections or compression/expansions have been applied).

(a) The graph\'s equation can be written in the form

f(x)=1x+A+B

for constants A and B. Based on the graph above, find the values for A and B.

A=_______ and B=_______

(b) Now take your formula from part (a) and write it as the ratio of two linear polynomials of the form,

f(x)=Mx+Cx+D

for constants M , C, and D. What are the values of M , C, and D?

M=_____ , C=_______ , and D=________

(c) Complete the exact values of the coordinates of the intercepts of the graph.

x-intercept:___________

y-intercept:___________

Solution

a) the graph of 1/x has origin as centre

now the centre is shifted to 1,- 4

so there is horizontal shift of 1 unit to the right and vertical shift of 4 units downwards

therefore function becomes ,

f(x) = {1/ (x-1) } - 4

A =-1

B=-4

b) f(x) = {1/ (x-1) } - 4

as ratio of two linear polynomials can be written as

{1 - 4 (x-1) } / (x-1)

= (1 - 4x + 4 ) / (x-1) = (5 - 4x) / (x-1)

f(x) = Mx +Cx + D (please give correct form)

c) x interceot : plug y=0;

x= 5/4

y intercept : plug x=0 ; y = -5