SOLUTION: how do you sketch a graph of (i) f(x)= 2\x (ii) g(x) = x (iii) h(x) = 2x\2

how do you sketch a graph of 

(i) f(x)= 2\x

I'm not sure what you are using a backwards slash \
to mean, but I'll assume it just means a fraction
dividing line.  If it doesn't then post again telling
us what you mean by \.

(i) 


Get some points:

let x = -4, then , so plot (-4,-.5)

let x = -2, then , so plot (-2,-1)

let x = -1, then , so plot (-1,-2)

let x = -.3, then , so plot (-.3,-7)

We cannot choose x = 0, because division by 0 is not defined.  This means
the line x = 0 (the y-axis) is an asymptote, a vertical line which the
graph gets closer and closer to but never touches. Now plot some points on
the right of the y-axis, where x is positive:

let x = .3, then f(x) = f(.3) = 2/(.3) = 6.7, so plot (.3,7)

let x = 1, then f(x) = f(1) = 2/(1) = 2, so plot (1,2)

let x = 2, then f(x) = f(2) = 2/(2) = 1, so plot (2,1)

let x = 4, then f(x) = f(4) = 2/(4) = .5, so plot (4,.5)



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(ii) g(x) = x

Get some points

let x = 0, then f(x) = f(0) = 0, so plot (1,1)

let x = 1, then f(x) = f(1) = 1, so plot (1,1)

let x = 2, then f(x) = f(2) = 2, so plot (2,2)

let x = -2, then f(x) = f(-2) = -2, so plot (-2,-2)

Draw a line through these points:

 


(iii) h(x) = 2x/2

The 2's cancel and that's the same as f(x) = x, problem (2).

If that's not what you meant, then post again with more 
details on what you meant.

Edwin