Question

Define f: R|-->R by f(x)=mx+b.

a. Show that f is a linear transformation when b=0
b. Find a property of a linear transformation that is violated when b=/0

c. Why is f called a linear function.

Answer 1

so a is obvious...

Answer 2

I got c answered as well.

Answer 3

@eliassaab

Answer 4

\[f(2 x) = 2 m x + b \ne 2 f(x)\]

Answer 5

b. Linear transformations have to go through the origin

Answer 6

If B != 0 then the origin isn't included in the space which would be a violation.

Answer 7

B!=0 is that B vectorial?

Answer 8

factorial

Answer 9

@eliassaab what do you mean?

Answer 10

no he is saying if B not equal 0

Answer 11

A function is linear if
f(x+y) = f(x) + f( y)
and
f( t x) = t f(x)
If b is not zero neither is satisfied.